Everyone puts in their claims
WW spot 1 goes and either makes no claim staying WW1 or picks up who he wants and then goes to the back of the queue (WW14)
then number 2 goes, same as above unless his first choice was taken by someone before him, then it goes on to his second chocie if he has one and so on.
your claim priority is by the order you put forward a claim, unless you "change priority".
The time of when teams make a claim has no bearing on who gets who. Only the teams spot in the queue and their priority of claims effect it.
In the above scenario, presuming you made claims for Perine and Burkhead what happened is following:
Rhys had priority: 1: Burkhead 2: Perine
You had Priority either:
a) 1 Burkhead 2: Kansas 3: Perine
or
b ) 1 Kansas 2:Burkhead 3:Perine
or
c) 1: Kansas, 2: Perine 3: Burkhead
But basically Rhys was always getting burkhead over you. You then priorotized (possibly by accident) Kansas over Perine so took them next, leaving Rhys to then get perine