I doubt that there is only one correct way to play a tremolo. If you listen to professional recordings of classical players and all the way to bluegrass players and all kinds of music inbetween, listening closely to their tremolo's, there is a wide variance in style and "attack." It all comes down to the sound that you want, and the piece of music that you are playing. Quite frankly, as a beginner, when trying to make a tremolo where the sounds are so closely made together that it almost sounds like one sustained tone, I doubt very much that you can get the kind of control to pick two strings down, one string up.
For now, just concentrate on achieving a smooth pick motion, both up and down, striking both strings, with increasing speed, and practice on it each day. Preferably using a metronome so your up and down strokes are consistently smooth and of the same speed and loudness before moving up to a higher speed.
A tremolo isn't a technique that is perfected in a week, or a month, or even in a year. After you get the basic tremolo down to your satisfaction, THEN try an advanced technique of two strings down, one string up. THEN try a tremolo using four strings, instead of two, etc. THEN, try how you do the tremolo based on the tempo and style of the song you are playing...slower songs with a slower tremolo, faster songs with a faster tremolo, etc. Or, then try tremolos that have no open strings (all fretted strings), and play an entire song with nothing but a tremolo and no single notes at all!
What I'm trying to say is that there is a lot of "technique" that goes into a tremolo, and many different ways to play it. Get the basics down, then move on to more complex or "advanced" tremolos. Above all, don't get discouraged. I doubt that there are many on this forum who would not tell you that it took them years of constant practice to really get good with tremolos, so don't expect that you will get good with them either until you have practiced them over and over and over...
And welcome to mandolins!
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