would we just add the timelock into the transaction message m in each adaptor signature?
Yes, the timelocks are incorporated into the transactions similarly to HTLCs. Specifically, the timelock can be included in the transaction data or in the adaptor signatures themselves to ensure that the time conditions are respected. By integrating the timelock into the transaction message
m, you ensure that the time constraints become an integral part of the swap agreement, allowing the involved parties to perform claim or refund actions
If so, is anything different from how it is in HTLCs, or is all we need still tA > tB?
The condition that tA is greater than tB remains in place to ensure the security of the atomic swap. This relationship prevents scenarios where one party could exploit the system to improperly obtain funds. Therefore, it is still necessary to maintain the hierarchy of timeouts to ensure that, in the event of a failure or aborting of the swap, each party can safely perform a refund. There are no fundamental differences regarding tA > tB when comparing PTLCs with HTLCs