You are clearly confused. NE555 that you mention clearly shows that chinese unit is a switching one. Quality switching unit would contan inductor, but with slow elements like LM358 and NE555 switching freqency must be rather low, so one would need big (read expensive) inductor. So you probably have plain PWM unit. Such unit is fit only for driving LED-s that have integrated resistors (most consumer lights seem be like that) and which are (at least approxiatly) matched to your power supply. That is 12V LED still needs 12V supply. If you used 12V LED with 13.8V supply, then you get much higher current than expected.
Concerning design, with 2 mosfets in parallel switched fully on you expect resonably current sharing, so nominally 15A per mosfet. With nominal Rdson of 0.006 Ohm, we get 0.006*15^2 = 1.35 W per mosfet. However, at that power mosfet will get hot and Rdson will grow, say double (when junction temperature is 175C). Then we get 2.7W, which is too much for TO-220 without a heatsink. Howewer, at 12A per mosfet we get 1.78W, which gives some margin for unequal current sharing. So, 30A is short term rating, 24A (that is 12*2) is reasonable max. For reliable long term operation I would prefer better margin. I would say that 10A is quite conservative. Above was assuming unit fully on. When duty cycle is less than 1, power loss is proportionally reduced, so we have less heat.
Concerning voltage, LM358 and LM7805 are rated for
30V, so no problem here. Mosftes have 70V rating, also OK. NE555 has lower rating, but presumably it is supplied by LM7805 so no problem with overvoltage here.In info you gave the only suspiciuos part is 7805 regulator. Namely, we need some voltage to control gates of mosfets. 5V is too low (Rdson would increase).
8V would be enough and 7808 could easily make it from 12V input so 7808 would be more natural. There are other possible sources of gate control voltage, but if circuit uses 5V then maximal current would be reduced (10A still should be OK).When LED is for lower voltage then your supplay, then you can use PWM circuit as long as peak current trough PWM circuit is limited (by LED and supply) to safe value (say 24A), but clearly this lowers possible power of LED much more than decrease in voltage would suggest. Current trough LED grows quickly with voltage, so nominal current of LED at its nominal voltage must be much smaller than
24A to make sure that it will not increase 24A at increased supply voltage.Now, what went wrong? Some possibilies are:
1) units were defective, possible but IME quite rare with chinese selers 2) design error like too low gate voltage or too limited heat dissipation trough case 3) your 13.8V coused much larger peak current, 4) your LED has some electronics inside including nontrivial filtering capactior(s), in such case you can get fairly large peak current 5) very high ambient temperature 6) other like surge, short in load etc...Now, except for 1, 4 and 6 it looks unlikely that other reasons alone would cause failure because at nominal
8.5 there is considerable safety margin, but combination of them together may be enough.Anyway, I would expect good seller to have clear instruction with warning that power supply should be matched to LED-s.