The Garrison Campaign chapter In Pursuit of Gul’dan that was added in 6.2 as part of Tanaan Jungle is indeed on a weekly cooldown, so if you’ve just completed one part the next won’t be offered until after reset on Wednesday.
It is separate from the 6.0 Garrison Campaign so you can do a part of each during the same week, but you would need to wait to get the next quest in the chain.