It has been almost a game month since the Thieves Guild tribute chest restocked. In another question someone said it usually takes about a week. Do I have to do more jobs to trigger an event? I notice that Delvin still had some even though I became guild master
Delvin and Vex will never run out of job. If the tribute chests behaves the same way as other respawning containers, you will need to avoid entering the Cistern for however long it takes for the container to respawn. Entering via the sewers is a good way to still get and return the jobs without passing the Cistern. The tribute chest does indeed respawn after a length of time has passed without the player entering the Cistern.
Also, as you complete jobs for Delvin and Vex, new baubles will be added to the guild master's "office". I believe you need to do 125 jobs to unlock all of them. The objects will be the things you are sent to steal during burglary and heist jobs.