I’m working on the integration and can try to answer your question.
As Dom explained, the IC will pull in blocks and verify that they are correct (i.e., well-formed, correct difficulty, …) and process the transactions after a certain number of confirmations.
Since the IC replicas pull in blocks from the Bitcoin network directly, the security depends on the correct functioning of both the IC and the Bitcoin network (but not on anything else).
In some sense, this still only gives you a “bridge”. The more exciting part is that canisters will be able to have a shared ECDCA key (sharing the key using threshold cryptography, see also here) so that a canister can securely hold Bitcoin (or Ether) itself! The Bitcoin (and Ethereum) state is then mainly used to keep track of the current balance for each canister that holds Bitcoin (and Ether).
Does this answer your question? If you have any follow-up questions, please let us know!