This is an interesting balance question either way you rule it. I think the intent was for spontaneous use, but I think RAW is for non-spontaneous use for prepared casters.
Balance-wise, let's look at both.
First, all interpretations give the advantage of not increasing the spell level and this advantage is just as good for prepared casters as for spontaneous casters. But, what other advantages does each interpretation have:
1) During Casting. Advantage Prepared Casters. They get the additional advantage that they get to do spontaneous metamagic. Spontaneous casters already had this benefit.
2) During Preparation. Advantage Unknown. Possibly an advantage for Prepared Casters or possibly a limitation for Prepared Casters: DM dependent. They get to cast 3 spells per day this way, but there is no limit to how many total spells they can prepare this way (by RAW). Presumably, the number per day prepared is the same as the number per day cast (RAW does not explicitly state this), in other words 3 per day cast and 3 per day prepared. However, over a long period of time, they could prepare all of their spells with the rod and either a) pick and choose at casting time which spell to metamagic (effectively making it on the fly and an advantage) or b) the first three they cast that were prepared as metamagic are metamagic, however, the DM then has to either allow additional metamagic prepared spells to be cast as non-metamatic (a limitation because the metamagic had to be used on the first 3 cast and not on any other), or the caster cannot cast those additional metamage spells at all (also a limitation) since the rod limits it to 3 cast per day and the 50 spells were already prepared as metamagic.
If one literally rules like Hyp and Thanee that it is during preparation, then metamagic rods are not well defined for prepared casters. There is no language that the metamagic from the rod disappears after 24 hours or some such, so literally one is almost forced to interpret (without additional house rules) that if it is at preparation time, then a caster can have 50 such prepared spells. Reading it literally for preparation time and then not reading it literally for preparation (times per day) is not consistent. Either one rules per literal RAW, or one does not. But, this results in adjudication issues.
Either way (#1 or #2 above), the item might have an additional advantage for prepared casters. But, there is nothing wrong with that. Just like a Ring of Wizardry cannot be used by a Cleric, there is nothing wrong with an item that is only useable by some classes or even is more worthwhile for some classes than others.
But Hyp's literal interpretation (if extended to the logical conclusion) can potentially result in adjudication issues where each DM rules something different.
Plus, the language of the item has an implication for during casting time as well:
All the rods described here are use-activated (but casting spells in a threatened area still draws an attack of opportunity).
The word casting in this sentence can be interpreted as referring back to use-activated for all uses of the Rod. It is not required to interpret it as Thanee did earlier in the thread.
Finally, WotC repeatedly has stated that during casting time is the intent. Since that is what WotC is stating and that has no adjudication issues, the "at preparation time" interpretation is more literal, but not WotC intent and not as clear.
A middle ground of "during preparation" but limited to 3 total spells prepared is more balanced, but that is not what RAW or WotC states.