Not in regards to who pays the contract. It's just a contract like any other.
You're right, but, a franchise tag is a fully guaranteed contract the minute it is signed.
© If a player subject to a Franchise Player designation accepts the Required Tender, theresulting Player Contract shall be fully guaranteed if the player’s contract is terminated because of lack of comparative skill;
So, what's being said is that, even if the player is injured, doesn't play, etc, his contract is still fully guaranteed. When we look at the rules for trading a player:
What happens if a player is traded or retires?
Answer: We already know that if a player is waived on or before June 1, the remaining signing bonus that has not been included in salary “accelerates” and is included in that year’s team salary. Acceleration also occurs when a player is traded or waived and picked up by another team. The new team is not responsible for any of the original signing bonus. The team that waived or traded the player is responsible for the accelerated signing bonus (in the same manner as described above).
Given that the franchise tag is seen as a fully guaranteed contract, the new team is not responsible for any of the original signing bonus (or, in this case, guaranteed money).