Do tweeters with open rear chamber need enclosure?

I would check and see what the tweeter manufacture recommends but separate enclosures have several virtues. That said, every case is different and the ideal isn't always the most practical.

If it doesn't have a sealed back,I would worry about the woofers back pressure causing damage to it.Also, I think the constant pressure changes would move the driver in the tweeter,causing distortion or some sort bad sound results.

What tweeter do you mean ? 99% of current design have sealed rear chambers.