any tyre company can do the tracking, they just need advice as they often dont know how the system works.
In theory at least adjusting the tracking due to replacement track rod should not alter the centring position.
Get the tracking adjusted by altering the length of the track rod (the one behind the axle) and if the steering wheel position is not correct afterwards, then adjust the length of the drag link to correct it, the steering should not pull either way afterwards. Do NOT alter the steering wheel to correct the position or you will have to hold the steering towards one side when going straight ahead.
The drag link length should not need changing more than 1/2 a turn, normally much less, if it does the tracking was either out before or it has not been adjusted correctly.
If the car steers straight without any bias (pulling) on the steering wheel the steering is centred correctly