Think of it this way, the state's jurisdiction for taxing things ends at its borders. If your boat isn't in the state they have no claim on it for taxing purposes.
The rules are highly variable in different states as to how long you can spend in their waters without needing to get a state registration in the new state. Many give you 90 days, some give only 30 or 60, and some say you should register your boat where you spend the most time within the year. Florida
requires all visiting documented boats to also be state registered, with no grace period.