全力ダッシュでこっちにやってきたメガネの男が放つ唾から弁当を避難させる。
The sentence above means 'A glasses wearing guy dashed here and made me move my bentou away from the saliva he released'
The question is, why is 避難させる used to say 'made me move my bentou'? Shouldn't させられる be used instead? させる means 'I made someone do something' if I am not correct
You could parse it this way:
［（全力ダッシュでこっちにやってきた）メガネの男が放つ］唾から弁当を避難させる。
全力ダッシュでこっちにやってきた is a relative clause that modifies メガネの男.
（全力ダッシュでこっちにやってきた）メガネの男
= a man with glasses (who dashed here)
全力ダッシュでこっちにやってきたメガネの男が放つ is another relative clause that modifies 唾.
（全力ダッシュでこっちにやってきたメガネの男が放つ）唾
= the saliva (which the man with glasses who dashed here releases)
メガネの男が is the subject of the verb 放つ.
The basic structure of the sentence is:
(私が)唾から弁当を避難させる。
lit. "(I) make my bento get away from saliva"
The subject of 避難させる is the unmentioned 私 "I".
The whole sentence literally means:
［（全力ダッシュでこっちにやってきた）メガネの男が放つ］唾から弁当を避難させる。
(I) make my bento get away from the saliva [which the man with glasses (who dashed here) releases].
I move my bentou away from the saliva ~.
させる is used because I make my bentou dodge it. The subject is not the guy nor his saliva.
I think a better translation for this might be:
The saliva released by the guy with glasses dashing over here (as fast as he could) made me move my bentou out of the way.
That is, it wasn't the guy making (forcing) you to move the bentou, it was the presence of the saliva which caused you to choose to move it, hence the causative of する.
