Yes, and this is something most people don't find out until the driver asks for it mid-journey which is why it's worth understanding before you book.
Whenever a tempo traveller crosses from one state into another, a state entry permit tax is applicable. This is charged by the state government, not the operator, so it gets added on top of your agreed fare. Every state has a different rate. For example, Himachal Pradesh, Uttarakhand, and Rajasthan all charge differently, and the amount also depends on the seating capacity of the vehicle.
The right way to handle this is simple: before finalising your booking, ask the operator to give you a full cost breakup that includes tolls, driver allowance, and state permit charges for your specific route. A genuine operator will always be transparent about this upfront. If someone is quoting you a flat all-inclusive price for an interstate trip without mentioning it at all, ask them specifically because it will come up during the journey regardless.
Before confirming any outstation trip, always look up the Tempo Traveller State Tax Rates for the states you will be travelling through. This one step ensures you know the complete trip cost in advance and there are zero surprises on the road.