Tuppy practise is the answer.
However I believe the solution may be simple.
Are you 'sighting' your fell correctly using the lines on your saw to help ?
As Edenarb mentioned it is not wrong to use the pushing chain to put in your felling cut - however you do need greater control of the saw in case it bucks around (or out) of the kerf. Are your horizontal cuts flat as a pancake, as most people when they are new to felling, lift the back handle up slightly which will obviously not give you a horizontal cut.
Marking the tree is a good idea -decide the correct size of your hinge (usually 10% for a sound tree) and make a vertical mark down the stem of where you need to finish your felling cut to maintain the correct size hinge (2 small 2" 'nicks' either side of the tree using your saw will do).
Now you can mark a horizontal line with your chain-brake on at the correct distance above the height of the horizontal cut of your directional notch (not forgetting the depth of your bar and chain).
Remember that if you make these marks they need to be accurate and you need to adhere to them when making your cuts. If using the pushing chain you can re-sight the fell (with the line you originally chose) and this will in turn maintain a hinge of adequate proportions that will be across the full width of the tree (as long as all the other cuts are of the correct dimensions).
Don't give up - it will come!
If you need to practise at home, go and get some 5ft stems, dig a hole in the garden and chock the stems into the hole making sure its secure (you could probably get 10 - 15 cuts into a single stem)
Wear you PPE - dont be tempted to do this without it!
I hope this is of help!
P.S. Thumbs round handles - correct you are not in control of the saw if you do not have your thumb fully round the handle.
P.P.S. Thumb on throttle - no problem with that as far a I am aware (also left hand holding handle at the point where the handle bends) this gives the best stability whilst cutting.