14nm at GloFo and I think it's 16nm at TSMC should come exceptionally quickly after 20nm at both companies.
While most places spend billions on R&D, then billions on equipment to get to a new process, 20/16 or 20/14nm were developed together. They will use almost entirely the same equipment, there is no refitting labs entirely or spending years and billions on new lithography methods. The 16/14nm from the two companies are keeping the same metal gate pitch which is basically 20nm(and afaik it will be noticeably smaller than Intel's 22nm gate pitch... which is much more important than most other things) with smaller 16/14nm features on other layers. So it will improve costs, yields, power usage and likely frequencies but with very little reworking of the fab to get going. Both companies have said for quite a long time that their 14/16nm variants are due within the year after then 20nm and there isn't much reason to think it isn't true at this stage.
Also I've heard that GloFo is already producing 20nm A57's for an unnamed customer, risk production is going on with low yields, there is usually a customer or two doing so. They'll have fab equipment going, not make certain of yields, often offer per good chip pricing(but still very expensive this early) and then they don't just pour money down the drain as they tweak the process but use a customer to do it. Apple couldn't rely on the output of risk production so would be fairly useless to them, but a smaller customer who would take anything they can get and release new products, particularly something using tiny tiny chips would be useful. If Apple can't count on X millions of chips per month then they can't launch a product, most companies don't have such high requirements.
A huge number of customers are skipping 20nm entirely because 14/16nm is where ultimately the process was designed to go with 20nm not being brilliant(nor bad) and because due to the extremely short time period between "processes" the cost of taping out at 20nm for most customers then almost immediately working on 16/14nm tape outs would be cost prohibitive. The few parts this won't be true for are for very high margin sales, so Apple selling their own devices that outmatch what anyone else can make, and gpu's which are so die size limited any drop instantly means improvement.... there are few to no other customers who required 350mm2+ chips at foundries outside gpus. Also makes gpu makers unsuitable for risk production as Nvidia well know. They tried to make runs of 480gtx's with risk production, but that is why it turned out they got extremely lucky on the good die deal which then TSMC refused to do again for them
TSMC/GloFo would do risk production for tiny chips as you'll still get enough off a wafer, when its a 500mm2 part and you're talking 2-3 good dies(if lucky) then it's just not worth it at all.
In terms of AMD taping out products, the link doesn't actually have a quote saying anything other than AMD working on 20/14nm products.
I would expect they would have started work on 20nm gpu's and 20nm apu's and 20nm cpu's quite some time ago, but they will have more products to do as well. I would think ps4/x1 shrinks will be far quicker than previous consoles(particularly with rumours of Sony thinking of a MUCH shorter generation for consoles this year, they want the PS4 cheaper asap, sales growing at lower price and then seemingly a new upgraded box in probably at max half the time the PS3 was around).
Pretty much the second 20nm parts are being shipped to AMD they'll be working on taping out 14/16nm products.