Hi Sulekra!This is first conditional, for the reasons you mention yourself.
Another way to differentiate between the two: In a zero conditional sentence you can use "when" instead of "if" without any difference in meaning.
In your examples if you change "if" to "when" you have the sentence
"When you see Michaela, ask her to call me."
this implies that you are definitely going to see her
"If you see her, ask her to call me" implies that it �s not certain.
As you see there is a difference between the two. So, it �s first conditional.
HtH!