AP gives 30 TP every 5 seconds.
This is 30TP every 3 seconds. Wow, such BRD. So it will be one more action every 6s.
At 0 TP, you can do one action every 3s and stay at 0TP. With Paeon, you can do one action every 2.5s (+20% DPS) and regen your TP by 15 every 3s. Let's take a example : a Bard, with 60 TP left, spamming "Straight Shot" during 60s.
Without Paeon, he will attack 20 times (3s between attacks) and after this minute is still at 0TP.
He starts by casting Paeon (3s) and keeps it during 6 ticks (18s).
0-3s : no attack.
3-20.5s : 7 attacks with -20%. He got 60+6*90 = 600TP and used 420. He's now at 180 TP.
20.5-21s : he removes paeon during the GCD.
21-58.5s : he attacks 15 times and has 0TP after his last attack.
Total : 7*0.8+15 = 20.6 attacks (20 attacks at 80% potency + 5 attacks at full potency). This bard is doing more DPS.

Next time you want to talk about "math", don't try to fool people with false informations.