Yeah, it means you are very mad about that man.

Actually the sentence has a stucture "一 A ，就B“，which means once doA, B happense. 一 is ommited sometimes。 When you use 一， it's like you do A and then immediately do B. When you don't, the two things are not giving a impression of immediately as when you use 一。 你一跟我讲到这个人，我就一肚子的火。 same pattern 我一回家就洗手。 我回家就洗手。 我一洗完澡就睡觉。 我洗完澡就睡觉 我一上课就想睡觉。 我上课就想睡觉。 for 一肚子的火 （it serves as a adj) 一肚子的火=very very angry 你不要吵我，我现在一肚子的火。 今天堵车了，开车开得我一肚子的火。 他不停地叫，叫得我一肚子的火。

是非常生气含蓄的表达

it means 我就会生气

yes,you are right