Is an employee considered to have fulfilled the trust if they use part of the money allocated for phone insurance to buy a computer without the manager's knowledge, with the intention of paying for the insurance later from the same account?

An agent must be trustworthy and act only with the permission of their principal. What you did, taking the remaining amount without permission, is not correct. You should have informed the manager and sought permission to borrow and repay. Now, you must repent and return the remaining amount to the institution. If the bills are due, you may use it to settle them.