If the character had polearm master he could follow this up with a bonus action attack with the butt of the spear for 1d4+strength.
Is this a correct interpretation of the rules?
Not quite, as far as I can tell the post-errata feat reads (bolding mine):
"When you take the Attack action and attack with
only a glaive, halberd, quarterstaff, or spear, you can use a bonus action to make a melee attack with the opposite end of the weapon. This attack uses the same ability modifier as the primary attack. The weapon's damage die for this attack is a d4, and it deals bludgeoning damage."
So if one of the attacks is not with a glaive, halberd, quarterstaff, or spear then the bonus action attack isn't kosher. Now I'm working from my own earlier print copy of the PHB and what errata I can find. If someone has a an absolutely authoritative text that lacks the "only" then I'll happily stand corrected. The second google hit for "polearm master" is an entry at
Home - D&D 5th Edition that doesn't have the "only", but then it also doesn't have the errata'd in second sentence and references to spears, and has other things that seem to presumably be someone's own unofficial wording.
My own Fighter/Barbarian character is very fond of making mixed weapon series of attacks, and would love for this not to interfere with his blunt end spear attacks, so I'd love to be wrong on this. Though usually the mixed weapon attacks have to do with throwing weapons or handcrossbows. This does bring up the interesting wrinkle that polearm master does not say the attacks on the action have to be melee attacks, so if one throws the spear at an enemy there is nothing to stop you from picking it up and making the blunt end attack as a bonus action in the same turn (though unless the first attack broke the enemy's concentration on a spell that was hampering your movement I can't think of when that would ever make any sense).