As someone pointed out, the dog's owner never called the OP back, so how many days should he have sat at that gap waiting for the dogs' owner to come along or return his call? I think did nothing wrong... except perhaps to allow the dogs to follow him. As someone else said, 3 beagles in the woods are probably hunting dogs and should be left alone or discouraged from following you.
I saw a thread on FB recently, where someone "saved" a dog that was loose, and moved out of state before realizing they couldn't keep it (I forget why, but it doesn't matter in this case), THEN they tried to find the original owners...
I'm not saying there aren't any cases where a dog found by a road somewhere doesn't need saving. My dog of 14 years was one of such. But that goes beyond this thread/ forum's scope. If a dog of a hunting breed tries to follow me on the trail when I'm out of state hiking, I'll discourage it from following me rather than adopt it as my new friend or taking responsibility for it. If I come across a dog on the trail that doesn't appear to be a hunting breed, but possibly a local's dog that got out or a hiker's pet that wandered off - and has no collar to identify the owner - I still believe the dog has a better chance of getting back to the owner with its nose rather than with mine.