The transaction manager (as implementation of the JTA specification) makes transparent a work above multiple resources. It ensures all the operations happens as a single unit of work. The "work above multiple resources" mean that that the application can insert data to database and meanwhile it sends a message to a JMS broker. Transaction manager guarantees ACID properties to be hold for this two operations. In simplistic form when the transaction finishes successfully the application developer can be sure both operation was processed. When some trouble happens is on the transaction manager to handle it - possibly throw an exception and rollback the data changes. Thus neither operation was processed.
It makes this transparent for the application developer who does not need to care to update first database and then JMS and checks if all data changes were really processed or a failure happens.
In general the JTA specification was not written with microservice architecture in mind. Now it really depends on your system design(!) But if I consider you have two microservices where each one has attached its own transaction manager then the transaction manager can't help you to sort out your concurrency issue. Transaction managers does not work (usually) in some synchronization. You don't work with multiple resources from one microservice (what is the usecase for the transaction manager) but with one resource from multiple microservices.
As there is the one resource it's the synchronization point for all you updates. It depends on it how it manages concurrency. Considering it's a SQL database then it depends on the level of the isolation it uses (ACID - I = isolation, see https://en.wikipedia.org/wiki/ACID_(computer_science)). Your particular example talks about lost update phenomena (https://vladmihalcea.com/a-beginners-guide-to-database-locking-and-the-lost-update-phenomena/). As both microservices tries to update one record. One solution for the avoiding the issue is using optimistic/pesimistic locking (you can implement it on your own by e.g. timestamps as stated above), the other is to use serializable isolation level in your database, or you can design your application for not reading and updating data based on what is read first time but change the sql query having the update atomic (or there are possibly other strategies how to work with your data model to achieve the desired outcome).
In summary - it depends on how your transaction manager is implemented, it can help you in a way but it's not its purpose. Your goal should be to check how the isolation level is set up at the shared storage and consider if your application needs to handle lost update phenomena at application level or your storage cang manage it for you.