No, withdraw assets from the vault does not affect the reward boosting timer. Only when you claim your time is reset.
Why do I have two reward amounts?
The rewards area shows two amounts, the amount on the left is the one that can be claimed immediately and the amount on the right is the total amount that can be claimed after 28 days of entry into the vault. If the user claims before the 28 days, he will forfeit part of the rewards, which will be distributed to the remaining vault participants.
If I claim my rewards before 28 days I forfeit a portion of them?
Yes, the reward boosting system's locking period is 28 days so there is no penalty on rewards.
Can I withdraw my assets from the vault without claim rewards and then claim rewards after the 28 day period?
Yes, if you do this you will not lose any rewards because the timer will be full after 28 days.
If I have the full timer and withdraw and deposit back into the vault is my timer reset?