Verifying Your Own Transactions With Umbrel vs. Wallet Server

I recently set up my Umbrel which is working well. I am working on connecting a hardware wallet using Specter Desktop and have a question about how I would use my node to verify my transactions. I understand this is one of the benefits of using an Umbrel.

In Specter
In Specter I connected my node following this post here which was very helpful Ledger hardware wallet.

Now I am at the step of connecting my hardware wallets. Once the wallet is connected and I send/receive BTC to the wallet addresses in Specter, does my BTC node and Umbrel take care of the rest and verify the transactions? I understand using my own node means I do not have to use a third parties servers to verify transactions on the Bitcoin network. I’m just making sure it’s this simple and I am not missing a step that is required to verify a transaction. Any help would be appreciated.