You are ignoring a very important part, which is that PTLCs typically combine adaptor signatures with multi-party signatures (like MultiSig)

"Adaptor signatures alone often cannot fully guarantee a contract... This issue is usually resolved by combining adaptor signatures with multi-party signatures. For example, Alice deposits her funds into an address that can only be spent if she and Bob collaborate to create a valid signature" 

So, in your example, when Alice disappears, Bob does not need Alice's tweak \(t\) to execute his refund. After the time \(t_B\), Bob can use a separate pre-agreed refund transaction path that does not require completing the adaptor signature. This refund mechanism would be built into the initial setup of the swap, similar to how HTLCs handle it

This is why documentation notes that adaptor signatures typically require "a time-locked refund option in case one party refuses to sign." The refund path is separate from the adaptor signature path used for successful execution of the swap