I think what you mean is to add angle to the E string, not tension. tension would change pitch and you still have an E so the tension is the same but the angle makes a difference.
My former luthier (not mine per se) recommended me to put as many wraps to increase the angle with the nut.
Never had a staying in tube problem. I have MIM basses not the best quality but NEVER a problem.
He is talking about adding downward tension over the nut, nut tension on the string.
Well, on guitar, the goal is to have as few wraps as possible to avoid slipping and stretching, especially with whammy bar use.
You usually pull the string through the hole around backwards and tie it in a knot around the peg, that way you get get less wraps without slipping.
Some locking tuners can manage like half a wrap around the peg because the peg itself clamps down on the end of the string so it won't slip.
If you are trying to get extra downward tension over the nut, try using a retainer bar or something.
Should see the body soon and the neck in a month or so.