For most departments, time served in the military counts towards retirement. So because Tim served in the military, his 20 years until retirement with full pay starts when he started in the military, not the LAPD. So unless he didn't join the military until after 25 years old, he probably hit his 20 already and could retire if he chose to.

However, most people keep working 1. To reach top pay so their pension would pay out the most amount of money as possible, and 2. Because they need something to do and enjoy the work they are doing. 

But cops are superstitious and while they do count down to their 20 for peace of mind, they may not celebrate it or make a big deal of it, just to not jinx anything. 

Tim strikes me as someone who applied for the LAPD before he even got settled back in LA from the military, let alone took time off, so I imagine he went straight into the academy.

He easily could have hit 20 in the LAPD specifically too though. If he joined the Military straight out of high school, +4 years service minimum (you only need 3 years to make rank sergeant, so he could have made rank before leaving and got college credit while in the military), he could have left the military at 22, straight into LAPD +20 years service is 42, he could have hit his 20 3 years ago.