I use trays, do not use any stop between developer and bleach-fix, and never have any problems. I do, however agitate the print vigorously as soon as it is put in the bleach-fix.
Is the developer you are using straight developer or replenisher? If it is replenisher, the cyan cast you initially experienced may be due to the fact that you did not use starter. Replenishers lack chemicals (bromide and/or chloride) that is necessary to inhibit fog formation that straight developer will have. I have mixed my own home-brew RA-4 chemistry before without any sodium chloride (the fog-inhibiting restrainer, which would found be in the starter) as an experiment and got a cyan cast. After adding the chloride the cyan cast went away. As development takes place, the chloride ion is produced as a by-product of development and slowly builds up in the developer, and eventually the cyan would go away on its own. Sounds like what happened to you.
I use Kodak RA-RT replenisher without any starter and have no problems, but use it at room temperature and have not used your developer. At higher temperatures the starter may be needed.