I will give my opinionated answer based on roughly 15 years of guitar playing which is personal experience and not rules or anything. Take it for what it is.
For most part I just consider everything from a major key perspective. Thus modes are basically useless. Additionally if you learn major scale in position style on neck, you will start on different notes. I feel modes are heavily related to this position method.
I find I only get a mode feeling if I play notes directly above and below the mode tonic then pause on tonic. Or as your teacher said their is some harmony like a chord, or even a single note drone in background.
But really I view it all as a major key. So d Dorian is just c major to me. A Ionian, c major. A minor pentatonic c major. D minor pentatoni, c major. A major pentatonic, c major. They are all constructed from c major.
Now some keys may share these subsets and then those keys are related or just share a common notes a lot. But I think most significant sound forces will be phenomena from the underlying major keys intervals.
And now that's what is important, intervals. Not just random intervals like only playing sixths. Buy ddiatonic intervals so that you stay in a key. What role and sound does the fifth play? The sixth? The forth? Etc.
Then you can view some more interesting stuff that doesn't fit a key but is close with substitutions. Also circle of fifths can be used to view modulation and key changes.
Note this is a bit more composed approach. It might be in wieldy for improve. Some times playing a relative minor over a major key might sound interesting, not too significant and is somethimg to play on spot that works out.
That's my take on it. Black bla school of music might disagree and id love to learn more on it but that's what I've taken from it all.