Recently, I've noticed pets are not where they are supposed to be.  For example, if a Gryphon goes from Big Field to Creek, the next turn I place a catcher in Big Field, yes?

Well, here is what I have gotten for the past few turns.

Mar 24, 2013 10:04:38 There's no one at Big Field.
Mar 24, 2013 06:04:31 There's no one at Eastern Fields.
Your catcher saw how a Gryphon flew from the Cave to Creek.
Your catcher saw how a Cockatrice came from the Eastern Fields to Waterfall.
Your catcher saw how a Gryphon flew from the Big Field to Waterfall.
Mar 24, 2013 02:04:46 Your catcher saw how a Dragon flew from the Eastern Fields to Creek.
Your watcher catcher was observed by a Dragon at the Creek.
Your Watcher Catcher was attacked by a Dragon at the Creek. Fortunately, no one was hurt.
Your catcher saw how a Unicorn came from the Big tree to Waterfall.
Your watcher catcher was observed by a Unicorn at the Waterfall.
Your Watcher Catcher was attacked by a Unicorn at the Waterfall. Fortunately, no one was hurt.
Your catcher saw how a Cockatrice came from the Magic Glade to Eastern Fields.

no, the next time it would be in it's den, which for a puma could big tree, magic glade or heart of the forest

Oh, I thought it alternated between hunting and watering until it fought with another creature?

I may be mistaken, though.

They alternate between all 3 in a cycle