What is the meaning of put us on deals?

It means that the staffer allocated work on deals (whatever that work consisted of, I've never worked for Goldman Sachs) to the junior members of the workforce.

The same turn of phrase is used for being allocated to any task in any environment. For instance a team of garment workers might be 'put on the new season's blouses' meaning that they would be making those blouses until they were 'taken off' them. Similarly a second line call centre worker might be 'put on complaints', a police officer might be 'put on traffic duty' or a water company employee might be 'put on sewer blockages'.

Sometimes someone who is sick or has been injured while doing the job can be 'put on light duties' when they return to work meaning that they aren't expected to lift anything or put themselves at risk.

The “on” in the Cambridge dictionary’s example: “Doctors put her on antibiotics”, i.e. "to put someone on something" means to order that someone start” is the same “on” as in “And my staffer who put us on deals,”. It means to start someone doing something, or to allocate something (an object or a task) to someone.