That's great that you have 20 month old son who has grasped the concept of time outs!
Impressive!
Same concept as being in the house. Let him know that he needs to be good in the store. Make sure you always have good manners in a store, too. He hears how you talk to others and will emulate that. My kids usually left a big shopping trip with some trinkety toy (for my son, it was ALWAYS a hot wheel.) A few times we left without that small toy because they were not deserving of it. It was missed. If they do misbehave, give a warning. Give them a time-out, without an audience, taking away any bankie, pacifier, anything for a minute or two, even holding them so that you are looking at the back of their head, if that's the best that you can do for a time out. When time out is done, make sure they know WHY they were in trouble, have them say, I'm sorry and just tell them, once again, what you expect. Try to use positive reinforcement before it gets to all of that.
I once left a shopping cart in an aisle at Target, filled with stuff for my kids, because I gave them fair warning (5 1/2 year old-Daughter and 2 1/2 years old-son. With a little drama, I grasped my daughters hand and carried my son out, under my right arm. I didn't yell, just calmly stated that our shopping trip was cancelled and now we have to go home. To this day, they remember it. (You only have to do it once if you act swiftly!)
My goal as a parent was to never be THAT parent, standing over a screaming, kicking child in the aisle of a store, saying "Honeyyyy, please get up!" My kids still like going shopping with me (13 and 10). I do enjoy their company in a store, too. It's amazing how many parents really dislike shopping with their kids. It's good you are laying down those ground rules. Good luck.