While it is possible to have tax due without actually selling something, usually via a 'deemed sale', that would not appear to be the case here. With a change in use from a principal residence to a rental property, you do indeed have a deemed sale. Even though you haven't sold the property, the change in use triggers rules that say that you treat it like you have. However, this is actually to your advantage, as any gain on your principal residence is not taxable, and you now have a rental property with a cost equal to it's current value (and not what you paid for it way back when). This means that when you do eventually sell it after being a rental property for a while, the capital gains you pay at that time would be less.
Two quick things to note:
1. The same rule does also work in reverse. If you move into a former rental and make it your own principal residence, you may indeed wind up with a tax bill based on the same 'deemed sale' provisions.
2. If you turn your principal residence into a rental, you may even avoid the capital gains tax on the rise in value for a few years, but this would require you to not have any other principal residence (ie, now be renting your own home). This is possible, but rather rare, so won't go there.