I suspect what you're talking about really depends on the actors and the type of theatre they're coming from. When you say "improvisers" does that mean they were changing dialogue? When they're doing that it's the directors job to guide them, the actors should also be aware that the performance has have a consistency (or at least enough) so that it can be cut together. Any theatre directors I've seen tend to create the performance in advance of the cameras rolling, so perhaps you could (if possible) have sessions in advance with your actors, rather than trying to do it on the day.
For the film we did earlier in the summer, our schedule was so compact that by the time we got to filming, we could only rehearse that very day (the packed schedule being my fault, another mistake I've learned from). And what I meant by improvisers was that they did change dialogue a little, but also they didn't really take my direction, which at some parts: it actually worked (example: I told one actor to pick up his wine glass midway through when he said his line in order to show his nervousness for meeting a character that had just entered the scene. He ended up not picking up the glass at all, which made me a little angry, but I stayed calm and did a retake of him taking the glass; the next day when I come to edit, I see he was moving his hands in a very shaky manner, what I notice some people do when they are nervous, and decided to go with it)
However, when it comes to doing dialogue scenes (in which we film from several angles), I give the actors a lot of direction, in order to maintain continuity. My film actor takes it perfectly, but the theatre actors are (naturally) more expressive with their hands, face, and body that I get a great performance out of them, but in the film room - things aren't too pretty. And these are above-average high school theatre actors, and my actors are either my age or a year younger, but knowing these guys, I highly doubt it's a power issue.
Nevertheless, I think my greatest fault was not having rehearsals and table talks with them before the shoot. And I have tried doing some improvisation with my film actor; only a few weeks ago, we did an action film, and I wrote zero dialogue on the script - I had him improvise the fight scenes (it was a shootout picture), and what dialogue he spoke. It turned out to be a pretty good film, but I think he's geared more for strict direction..
Anyways, thank you for your advice, I've got a film I'm planning to shoot in October with both theatre and film actors, and will definitely use these techniques in my direction.