The tour company should take care of the hotel bookings for all of your tour and it is very likely included in your price but there are exceptions. This is what you should consider in terms of hotel and flight bookings for your storm chasing tour.
Flights to the location of your storm chasing tour are NOT included in the tour price. You need to book it yourself and make sure you arrive in time for the tour.
All tour companies have different policies but most commonly is that you have for example 7 days and 7 nights meaning that hotel costs are included for all nights while chasing. The difference is sometimes in which night that is not included: the night between the Arrival Date and the Start Date or the night between the End Date and the Departure Date. Usually, the night between the Arrival Date and the Start Date is not included in your tour price but the night between the End Date and Departure Date is (but vice versa could be true).
The tour company will have arranged with a hotel close to an airport in the base city, usually with a discount, and will provide the information on how to book it in order to get the discount as well as which nights you are expected to pay for.