Also notice how dramatically they stepped up their campaign against KSA since Iran launched its aggressive campaign to lash out against economic sanctions.
There's no inherent reasons the Houthis should be launching sophisticated, high-impact attacks on KSA on a weekly basis. This sort of escalation makes no sense within their own geopolitical context, but makes perfect sense when you consider Iran's contexts and regional goals.
Same for Hezbollah group in Lebanon against Israel. All the recent tensions in that conflict can't be explained by the organic interests of the Lebanese nation or people. In fact, a conflict with Israel is against the Lebanese national interest and would lead to great destruction in Lebanon. However, Hezbollah is escalating and building up towards that very conflict.
The vast majority of Hezbollah's budget is contributed by Iran:
https://en.wikipedia.org/wiki/Funding_of_Hezbollah#Iran
Iran can ill afford to make that investment if they don't get much out of it, and it's pretty accurate to say Hezbollah is acting according to the interest of Iran far more than any other set of interests, including the Lebanese interest.
Hezbollah owes its power and arguably its existence to Iran. It's naive to expect it to act independently of Iranian interests.