Well, in your defense, its hard to play a creature smart when you aren't prepared for the encounter. Also, its rather unlikely that a single Noble Salamander in and of itself is going to present much of a challenge for a skilled party of more than about 8th level. The reason is that it is a low AC monster, and parties of 8th level or higher can generate a massive ammount of damage on low AC monsters.
In the case of the Noble Salamander, the things that stands out to me as strengths are +25 grapple bonus, constrict, and the high attack bonus combined with power attack. These are the features which are exceptional in a CR 10 opponent.
It's big weaknesses are poor manueverability and low AC. These are the features which are well below average in a CR 10 opponent.
His hitpoints are fairly average, and his spell casting ability is unremarkable.
All this paints a picture for me of a creature with alot of flexibility, but who tends to be overmatched against a specialist no matter what he does. He can't stand up and fight in a slogfest (low AC + unremarkable hitpoints), and he doesn't have enough spellcasting ability to trade blows in a ranged fight, and he's got limited ability to manuever to gain advantage. In other words, this is a creature that very much needs to have a prepared position to defend - and getting summoned into a fight is not all that great.
The way for a Noble Salamander to win is to get the opponent come to him, thereby allowing him to maximize the advantage of his reach (more AoO), his multiple attacks (he wants to take full attack actions), and his ability to nuetralize an opponent with his tail attack/constrict ruetine.
The way for a Noble Salamander to lose is chase a group of opponents, or otherwise get in a situation where he's swapping blow for blow. Note that generally speaking, casting one spell per round although it sounds attractive because the spells are so flashy is probably a way to lose because the PC's party will then be matching thier collective actions against the one action per round of the Salamander.
As a DM, you should always be aware that the advantage of the PC party is that thier combined actions per round and/or combined hitpoints generally exceeds that of any group of foes that they are facing. The way to make a fight tough on the PC's is to neutralize those advantages, by 'stealing' actions from the PC's or 'stealing' hit points from the PC's. In the first case, you want to get the PC's to waste actions doing things that don't take hitpoints from the monster, and in the second case you want to place the PC's in a position where they are all threatened by continious damage.
The noble salamander has several options for each. In the case of getting the PC's to waste actions, he's got a reach weapon. If he can 'trip' PC's as they move through his threatened area, or playing it safer if he can just take advantage of those AoO to just gain an extra 'virtual' round or two, then he's doing good. Also, if he can get the PC's to come to him, then he can match his full attack action versus the PC's standard actions or (better yet) charge attacks. The other nifty thing he can do is grapple an opponent, nuetralizing that opponents ability to act. The best situation for a grapple is either a) isolating a single PC, who will then likely be helpless against a grapple attack, or b) grappling a low strength/small PC and then taking a -20 on his grapple check (it would still be +5) in succeeding rounds forcing the PC to spend at least a round trying to escape and with bad rolls several rounds, while the salamander doesn't have to waste any actions.
In the case of stealing hit points from the PC, he's got several area of effect spells. However, evocation is generally a weak attack in 3rd edition. Although it is tempting to lauch fireballs at the party, this is only an effective strategy if the PC's have decided to pull back and try to force the salamander to come to them. In this case, the Salamander should first try to use Wall of Fire to gain cover - because even trading fireballs with the PC's spell attacks + ranged weapon attacks is a losing proposition. Once the Salamander gains Wall of Fire as cover, he can then summon a Huge Fire elemental or additional walls of Fire as further cover. This should force the Party to change tactics, back to a tactical situation that Favors the Salamander. The Salamander should only launch waves of fireballs if the PC party is unable to concentrate their actions on the Salamander (such as if they all are forced to deal with the elemental). Keep very much in mind that the Salamander is capable of fireballing his own position with no harm, and if he has oppurtunity to fight in a static position he'd very much prefer to prepare that position by positioning a wall of fire close behind him, forcing anyone engaged in melee with him to take continious damage.
Remember what I said about the Salamander needing a prepared position? If he can start the fight with a wall of fire behind him and a greater fire elemental in front of him, he's a darn tough CR 10 opponent. Add in a bit of treasure which improves his AC and a few minions, and he can make a very memorable foe. Without those advantages though, he's got a problem, and he probably can't afford to give the PC's two full rounds while he prepares his position. Depending on the shape of the room and whether he's got some space between him and the PC's, it may be worth it though to make his first action summoning up the elemental and hiding behind it as cover. Since it's huge, he may well be able to gain complete cover on the PC's. Even if this didn't occur to you, the fact that Monster Summoning VII is a 7th level spell normally available only to 13th level Wizards (CR 13) is something that you should notice.
Lastly, if the Party loses line of sight on the Salamander for some length of time, don't forget that the Salamander is pretty good at hiding for a CR 10 creature, and can set a new ambush to gain ('steal') a surprise round from an unwary party.
It would be very hard to come up with an easy answer to your question. I don't really know how good my disection of the Noble Salamander is, but I think its pretty decent. I'm known as a very harsh DM, so I think I'm probably pretty good at getting the most out of my monsters. Hopefully, by listening to me disect the Salamander, you've gotten some indication of what you should be looking for in the monsters description that tells you how to use that monster to its utmost.