Coming across lines such as (two separate contexts):
「ご飯をよそってきて食べなよ」
and
「そんなに驚かないで。頭を冷やすために下でお茶でも淹れてくるよ」
I'm having trouble understanding the usage of 来る in both of these sentences.
I was told that the former sentence, 来る functions as an auxiliary (which makes sense in the surrounding context, since it isn't indicated that the person being told needed to move between different locations), but am then a little confused what it specifically functions as (besides perhaps,"to come to serving their rice", "to start serving their rice").
The second sentence seems much more clear with 来る functioning as a full verb, "to brew tea and return", "to go brew tea", but with how I understand the first line, I started getting second doubts here and thought that it could function as an auxiliary also, "to come to brew tea", "to start brewing tea."
Is there a general rule of thumb for particular verbs used with てくる, or is it solely reliant on context? Any clarification would be greatly appreciated, as well as correcting any misunderstandings I might have with 来る.