If the DM's ruled that arrows for a longbow and shortbow are different, the DM should also rule that arrows for composite longbows and composite shortbows are different from those. In fact, the house rule may be even more challenging than that because the only way to use the rules as written to reach that conclusion is by consulting Table 7–5: Weapons (PH 116-7). That table lists separately bolts under each of the heavy crossbow, the light crossbow, the hand crossbow, the heavy repeating crossbow, and the light repeating crossbow, and lists separately arrows under each of the longbow, the shortbow, the composite longbow, and the composite shortbow. Under this reading, all bows and crossbows should use different ammunition if any of them do.
The DM may even think she's doing the PCs a favor by allowing them to use at a penalty arrows or bolts designed for the wrong kind of weapon! A stricter DM would've ruled the wrong type of ammunition is flat-out impossible to use with the wrong type of weapon.
TobyY. noted in a comment that the real-world advantage of a composite bow is its self-bow-like draw-weight and draw-length but a shorter bow stave, making it a safe assumption that longbows and composite longbows can share the same arrows, while Zeiss Ikon's answer discusses how some bows will be massively less effective with the wrong arrows. Either way, though, if the DM's relying solely on the weapons table, real-world evidence and experience don't matter.
However, this is a house rule
The game makes no distinction, so far as I am aware, for example, between arrows designed for a Medium creature's longbow and arrows designed for a Medium creature's composite longbow or shortbow. (Arguments can be made both for and against bigger and littler ammunition being required for bigger and littler weapons, but I'm pretty sure that's beyond this question's scope.)
The Player's Handbook, for example, in the starting packages has the half-orc barbarian, dwarf fighter, human fighter, and human paladin carry shortbows and the elf ranger carry a longbow, yet all carry just arrows. This is consistent throughout the game. No mention's made of needing different bolts for different crossbows or different arrows for different bows except in splatbooks that detail specific weapons. (Frostburn's bone bow, for example, says that it "is designed to fire exceptionally large arrows specially made for it" (75).) Even the hand crossbow's bolts cost and weigh as much as the heavy crossbow's bolts.
The exception is the repeating crossbows, both of which use 5-bolt clips of the same cost and weight that cost and weigh as much as 10 bolts for a hand, light, or heavy crossbow. (Even then, a solid argument can be made that the extra weight and expense isn't for the bolts but for the ammunition clips in which they're sold.)
Just to confirm, the Monster Manual's half-celestial paladin (144-5) has 10 silvered and 10 cold iron arrows and a masterwork composite longbow (+4 Str bonus), and the harpy archer (150-1) has 10 cold iron arrows, 10 silvered arrows, and 5 +2 arrows for her +1 frost composite longbow (+1 Str bonus). Neither entry designates the arrows as composite longbow arrows.
Finally, the Dungeon Master's Guide on Table 7–13: Common Ranged Weapons (223) lists different kinds of crossbows and bows separately but lists ammunition in simple lump sums of 50 arrows, 50 crossbow bolts, and 50 sling bullets, undifferentiated by the weapons intended to fire them.
Sometimes game designers omit what they assume readers will perceive on their own, and, y'know, sometimes readers just don't make the same assumptions the designers do, instead readers seeing what they want to see. That's not an insult, and maybe it's even become important for some reason: the DM may have big plans that hinge on this house rule ("Only the greatest of the halfling archers can slay the King of Storm Giants with this +5 giant-king-slaying Small shortbow artifact arrow!"). I don't know. I do know, however, that in such a campaign, unless playing a swordsman or wizard were equally complicated, I wouldn't try to play an archer.