I can't speak to all allies.
You're quite right. The U.S. response, which you would have seen very early on in Tacloban, is largely a result of the number of forces they have in very close proximity in both Guam and Okinawa.
If I look at other allies, we were certainly the first into Panay Island and the first ally other than the Americans that was there in any considerable capability. Allies were still coming in well after the 24th, depending on their direction and the response times of their forces.