the only time a redshirt will transfer is if you promised him a start or minutes then redshirt him, then he gets treated like any other player you break a recruiting promise to (I think they all transfer 100%, but I almost never make promises that I am unable/unwilling/unprepared to keep, so I am not certain if the transfer is automatic or just very likely).
Related info: if you promise a start/minutes and leave them til signings he will never accept redshirt - if you make then later cancel promises (by informing of redshirt) and leave that inform applied and sign him anyway he will always accept - if you cancel promises (offer a redshirt) and then inform of no redshirt (even in same cycle before effort runs) he reverts back to redshirt neutral status and makes up his mind like anyone who never talked about redshirt - as long as you don't forget to inform of no redshirt (of course informing of redshirt carries immediate negative recruiting value that can only be compensated for by other positive effort, (informing of no redshirt DOES NOT remove the negative effort) and if you aren't heavily invested enough at time of inform he may get pissy and no longer accept regular effort (HV, CV, etc), so its wise to frontload informs (send a few HVs one cycle, wait for them to be accepted and inform/uninform on the next cycle) or be very tight level before informing.