I guess all these ‘tricks’ are meant to help if you don’t know scales and intervals but it seems to me they complicate things more than anything,
A major chord is the root, major third and perfect fifth. The intervals of the third and fifth are found by counting the number of semitones from the root to the note. Once you know your intervals and scales, then it’s easy.
A major chord is always a root, a major third and a perfect fifth. A minor chord is always a root, minor third and perfect fifth. Always. This is the definition of these particular chords.
So you just need to look at the notes in the scale of the key and match them up to your chord and you see what you get. In the scale of F, the F is natural. So the third in the D chord is (D-E-F) is F natural. If you count the interval, you find that is a minor third (three semitones from the root). The fifth (D-E-F-G-A) in the F scale is a A natural, a perfect fith (seven semitones from the root). So you have root-minor third-perfect fifth, a minor chord.
But in the A scale, the third interval (D-E-F) is an F#. This is four semitones from the D and therefore a major third. The fifth interval (D-E-F-G-A) is a A natural and so, like in the F scale, that’s a perfect fifth. So you have root-major third-perfect fifth, a major chord.
Learning intervals and scales is not that difficult and you can make it easy on yourself and just start with the stuff you use, major and minor chords and simpler scales (I mean, when was the last time you played in F#?)
Sorry for the ramble but…
In fact, it can be even simpler. If you just know your scales and you know your chords and understand how chords are made, then you can just use the notes of the scale to make the chord and then look what you have.
So in F, a D and an F natural and an A make a D min. In A, a D and an F# and an A make a D maj.