Bath director of rugby Todd Blackadder said Watson underwent a second surgery for his injury and was a doubt for the 2019 Six Nations.
Joseph could return around Christmas.
"The initial surgery didn't take basically, (he needed)another tear to have surgery again. He's had to start afresh and it was done about a month ago," Blackadder told British media.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"JJ (Joseph) is still on track. He'll be somewhere around Christmas time... It's hard to put a timeline on these things."
The duo, who missed England's series defeat by South Africa, are set to be sidelined for home matches against South Africa, New Zealand, Japan and Australia.
A slew of injuries to players sustained during England training camps prompted a war of words between the national team's head coach Eddie Jones and Bath owner Bruce Craig in May.
Blackadder said he hoped to work closer with the England set-up to ensure players' health.
"There will be lessons learned on both sides on how we get the best out of all our players," he said.
"Hopefully common sense will prevail and we send players (to England) in the best possible nick they can be and we just hope that is reciprocated."
(Reporting by Aditi Prakash in Bengaluru; Editing by Ian Ransom)
