Swing is polyrhytmic, which means you have several layers of rhytm and music structure. The basic unit can be considered to be two beats, one two, one two, one two etc.
Then you have four beats to the bar. And you have two bars giving and eight count phrase.
All patterns wil normally begin on the one beat of the basic one-two pattern. I write 'normally' because there is a huge degree of freedom in swing. And it's possible to make exceptions. Although they shouldn't be too many, or they'll disrupt the feel of the dance. Which 'one' beat you start a pattern on, doesn't really matter.
Most swing forms have patterns of 4, 6, 8, 10, 12 beats and more, even though some has a base pattern of six beats like ECS and Boogie Woogie, while Lindy has an eight beat base pattern. I thin WCS is also considered an eight count basic. (If I mix count and beat here, it really doesn't matter. It's the beats you count.)
When dancin Lindy, with mostly eight count patterns, I tend to do most patterns in sync with the eight count phrases. This is easiest, and gives the best feel. However, depending on the music, my partner, my mood etc. There is no problem starting an eight count pattern on 3, 5 or 7. However, this does not feel as natural and comfortable, so usually when dancing I do this only for a while before settling back where each eight count mathces the 8 count phrase of the music.
Usually when I do Lindy, I do a lot of 8 count in sync with the phrases. Then I mix it up with different patterns of different lenghts, before settling back again. As I said, it depends on the music, my partner, and my mood.
When it comes to swing forms with a six count base and dominated by six count patterns, there is not the same natural sync to the eight count phrases of the music. Doing only six count patterns, the first step of a new pattern starts on 1, 7, 5, 3, 1, 7, 5, 3 etc.
What we have here is a six count rhytm out of phase with the eight count phrases. This gives a dual rhythm thing going, which is perfectly fine.
Even though the pattern above is not following the eight count phrases, it still matches the music. Note that it you begin on one again after each four six counts. That is after each third eight count phrase. (4*6=3*8=24 beats)
Incidentally, swing music is very often built up with three repeating eight count phrases with the fourth being different and often a break. So if BW or ECS dancers dances four 6-count patterns and doing an 8-count break, they will be in perfectly sync with these larger structures in the music. (These larger structures also repeats itselfs in swing (AABA) and blues (AAAABA) schemas, but I'm not going into that here.)
To sum up. Swing music has lots of different rhytms and structures in different layers. The basic unit is the one-two beats. How this is interpreted into the dance is a question of musicality, more than rules. There are no hard and fast rules you need to comply to, but there are some things that will feel more right than others.