| mdt |
Yes, it follows all the other rules that all other characters follow.
A human warrior with BAB +16 gets 3 attacks, and adds str to hit on all of them with a melee attack.
A lion gets two claws, a bite, and potentially a rake, and gets str added to all of them.
An eidelon with 3 attacks as a full round action gets str on all of them. Unless a class/race/etc calls out an exception to the general rules, the general rules apply. The eidelon doesn't have a call out exception, so it uses the normal rules. Str to BAB for melee, and Dex to BAB for ranged/finesse.