"Tune the perfect intervals with the open string. Some players also tune the third with the open string."
The perfect intervals (the 4th, 5th and 8ve) can always be tuned with a relevant open string. In this case tune A and E with the open A-string.
Different players have different opinions about whether to tune 3rds with the open string since doing so makes the major 3rd lower and the minor 3rd interval higher.
Make a decision based on the context. If the passage is a slow lyrical one it can often need a high major 3rd or a low minor 3rd.
However if it is part of a fast passage then slow practice tuning using an open string can help since we hear the interval almost as part of a chord and a mid-range position for the 3rd is useful.
Repertoire - for Concerto in A by Mozart