The saying, “The right tool for the right job” has been around a long time and for good reason.
Using a #2 bit in a #1 screw or vice versa may give results that are less than desirable. You have to give the bit a chance. It should go into the screw head to about where the shoulder or where the two angles of the bit tip and the shaft meet. Just inserting the tip partially into the screw head alone does not give the bit or the screw a fair chance of working properly, especially if you try to go fast.
Also not all screws that look like a Phillips are actually a Phillips. You may find a few others that migrated from overseas. Posidriv® and Frearson are a couple you might run into and while they may work, they are not Phillips. Always start your project with real Phillips screws. Please keep this in mind when using your KnifeEdge® Bits.