You have it right, and it does feel a bit backwards. The row number is a y coordinate, and the column number is an x coordinate, and yet we usually write row,col but we also usually write x,y.
Whether you want to write your array as [y][x] or [x][y] depends mostly on how much you actually care about the layout of your array in memory (and if you do, what language you use). And whether you want to write functions/methods that can operate on rows or columns in isolation.
If you are writing C/C++ code, arrays are stored in Row Major Order which means that a single row of data can be treated as 1 dimensional array. But a single column of data cannot. If I remember correctly, VB uses column major order, so languages vary. I’d be surprised of C# isn’t also row major order, but I don’t know.