How exactly do transactions with PHP PDO work with

I'm making a webapp where they'll be multiple users interacting with each other and reading/making decisions on/modifying shared data.

I've read that transactions are atomic, which is what I need. However, I'm not sure how it works with the PHP PDO::beginTransaction()

I mean atomic as in if one transaction is editing some data, all other transactions also modifying/reading that data will need to wait until the first transaction finishes. Like I don't want two scripts reading a value, incrementing the old one, and effectively storing only one increment. The second script should have to wait for the first one to finish.

In almost all the examples I've seen the queries are used consecutively (example PHP + MySQL transactions examples). A lot of what I'm doing requires

querying and fetching
checking that data, and acting on it, as part of the same transaction

Will the transaction still work atomically if there is PHP code between queries?
I know you should prepare your statements outside the transaction, but is it okay to prepare it inside? Basically, I'm worried about PHP activity ruining the atomicity of a transaction.

Here's an example (this one doesn't require checking a previous value). I have a very basic inbox system which stores mail as a serialized array (if someone has a better recommendation please let me know). So I query for it, append the new message, and store it. Will it work as expected?

$getMail = $con->prepare('SELECT messages FROM inboxes WHERE id=?');
$storeMail = $con->prepare('UPDATE inboxes SET messages=? WHERE id=?');
$con->beginTransaction();
$getMail->execute(array($recipientID));
$result = $getMail->fetch();
$result = unserialize($result[0]);
$result[] = $msg;
$storeMail->execute(array(serialize($result), $recipientID));
$con->commit();

Transactions are atomic only with respect to other database connections trying to use the same data, i.e. other connections will see either no changes made by your transaction, or all changes; "atomic" meaning no other database connection will see an in-between state with some data updated and other not.

PHP code between queries won't break atomicity, and it does not matter where you prepare your statements.