The English translation here should be in the present continuous, not the simple present (i.e. 'don't tell me he is escaping' instead of '...he escapes')
I agree with Vera. In English, the simple present tense "he escapes" is almost exclusively used for habitual actions that happen repeatedly, though not necessarily at the moment of speaking. (It would be used to describe a Houdini wannabe, or a dog that keeps getting out of the yard.) For an action that is actially happening now, we use present progressive "he is escaping."
Both להגיד and לומר are equally good in future/imperative/infinitive. "אל תגידו לי" = "אל תאמרו לי". Maybe in future tense להגיד is a bit more common, but לומר is very much in use as well.
Other way around surely? tagid li, never tomar li. I'm not complaining as I want to learn old and stuffy hebrew as much as I want to learn slang...
I agreed with you that תגיד is more common in future tense, all I'm saying is that תאמר is also used.