2 separate, publicly traded companies make their own decisions.
They might still work together, but the path PayPal takes will be determined by the new management and big shareholders.
They always had separate managements. However there finances were shared, therefore ebay was dragging the stocks down. This was part of the tec talk for months now, due to the new high competition for easy checkout. Paypal was trying to grow, but too much of it's revenue was being redirected to ebay. They still plan on remaining together, but splitting the finances.
Thus the recent changes in eBay's seller policies. They want to wicker out all the sellers that may scare away buyers, because they need to pick up the general trust in order to raise their own stocks.