The problem with classic time tracking
A separate time-tracking tool means one more login, one more tab and, in practice, a lot of people forget to start or stop it. The data becomes unreliable exactly when you need it to be accurate.
A simpler alternative
Instead of measuring every minute, log short work updates tied directly to the project and task, what got done, not exactly how long it took. For most small businesses, that's enough to understand where the team's time is going.
When you really need precision
If you bill by the hour, precision matters more. In that case, log the time right after you finish a work session, not at the end of the week from memory, memory always rounds in your favor, not the client's.
Bottom line
Choose the level of precision that matches your billing model, not the most complicated tool available. Simplicity wins most of the time.