when you use the pattern 動詞+起+object+來
it more like you are expressing a tone of progressive tense. ( past or present )
no matter 吃飯，打電話，or 下雨
it just a verb phrase.if translate these into english ,they will be:
have a meal,make a call and rain.
when you use these words in Chinese,people don't know when did (or will) these things happen,if you don't add a time .
because, in chinese,if we want to express" he had a meal yesterday",we just add a word that means yesterday in the sentence,like "he have a meal yesterday"
but translate 吃起飯來/打起電話來/下起雨來 into english
they will be
(sb) is (are /was/were) having a meal
(sb) is (are /was/were) making a call
it is (was) raining