If you look at the SS from about 22/11, you will see that each time Garfield has dropped to green numbers, he has shot up and bounced. On 2 occasions he bounced for 3 cycles and for one he bounced for 1 1/2 cycles before dropping down again. He also bounces from the blue numbers.
Watch the cycles (especially the second and third cycles of a bounce) and if you can see he is dropping down (if you get a +2 or a before bed test this will help you see what the cycle may be like) and if you think he is dropping low, then check more frequently and give some low carb food to "feed the curve" and let him come down more gently.
If you can help stop the fast drops, that will help stop the bouncing.
Some cats are bouncers. Sheba was a real bouncer and diver. Some cats bounce all the way to remission.
You are just new to testing, even though he is not a new diabetic, you are just now seeing what the BG levels do.
The more he can get into the lower numbers, the more his body will get used to these lower numbers and hopefully the bouncing will ease off or stop.