Tulip anemones typically max out at around 2 inches, and yours do look QUITE like them.
Here's an idea: get a bag of frozen mysis and hand feed one that is easy to reach. Give it one or a couple mysis every other day (depending on it's size) for a month or two. If it's gonna get big it'll do it. And if it's gonna split, it'll probably do that by then too.