How do I say "He already went to do X for me", implying he is still in the process of X, not finished?

Question

The other day at some festival a few japanese friends asked me something to the effect of アイスを買ってくるけど、行く？ But I had already asked a friend, who had not yet returned, to get some for me. So I said ジェームズがもう買って来てくれたので大丈夫。 What I intended to say in English was "No thanks, James already went to get me some." But it seems that the japanese version of that statement could have multiple meanings. How do I differentiate between "He already bought it for me (and has completed this process)" and　"He has already gone to buy it for me (and has not yet completed this action)"? (もう買ってきてくれている could be a possibility, but for some reason doesn't sound correct to me. )

Answer 1

When James has already completed the mission of buying ice cream for you and he has already come back, you can say ジェームスがもう買ってきてくれたから大丈夫.

When James is still in the process of buying ice cream for you and hasn't come back yet, you can say ジェームスが今買いに行ってくれているから大丈夫.