switching food brands

hi everyone random question!
so I am trying to change my cats food over to adult food from kitten food since they are both about 11 months old now, and I was feeding them blue buffalo for the last year. just this weekend I bought some wellness adult food and probably didn't do the best job transitioning the change. But I fed my cats one flavor of it and they ate it and it was fine, and just yesterday I fed them a different flavor or the wellNess and my one cat threw it up and had diarreha last night. He is a healthy cat, young, totally fine, and he is eating a lot today(of his old food) and acting totally fine. so would the reaction probably be from the new flavor? just want to see what anyone thinks! He hasn't pooped since the diarreha so not sure if it stopped but everything else is normal, I stopped feeding the wellness

Slow and steady is the key to changing cat foods. Usually flavors within the same brand and product line are easier on the system but any sort of sudden change in the brand (or even product line in the same brand) can cause the problems you mention. Your cats digestive system is used to the old food and the new food is a shock to the system. 

Any changes should be done over several days (I actually do a full month). The standard practice is 1/4 new food with 3/4 old food for 2 days, 1/2 new food with 1/2 old food for 3 days, 3/4 new food with 1/4 old food for 2 days, then all new food. Personally I keep their food in an airtight container in the garage that can hold 15 pounds of food, in the house I have a smaller container that is about 5 pounds. When I change foods I finish off the old food in the garage and just have the 5 pounds in the house. I will top off the container in the house with the new food every other day and mix thoroughly each time. So the ratio of old to new will slowly reverse as I add the new food into the mix. Usually I don't even notice the point when it is all new food only. You could do the same on a smaller scale by putting the last of the old food in a gallon bag. Add a cup of new food and mix well whenever space allows. If the kibble is different enough to tell the difference you will know when it is pretty much all the new food. If not, once you've finished a bag of the new food it is safe to assume they are on the new food. 

I personally mix even the old bags with new bags of the same food because there can be minor differences in batches. I have never had any tummy problems when switching foods nor have my cats ever rejected a new food (likely because they probably don't notice between the slow change and mingled flavors during the switch). If you are doing different flavors of the same product line you should switch flavors when the bag is done and still do a switch over the course of a week at least to prevent any problems with their tummies. 

In your case you've already made a change so it isn't worth going back because what is done is done. But give them at least 4-6 weeks for their tummies to settle before making any other diet changes and change slowly in the future.  

If you are talking about canned food vs kibble, some brands are just more rich than others and can cause issues.  Additionally, certain proteins (ie flavors) can simply cause reactions)  Many cats cannot handle fish in their diets, some are allergic to chicken, beef,  etc.  And depending on WHICH of the lines of Wellness you chose, some of those actually have some grains, I believe, and often cats are allergic to wheat, corn and/or soy, even dairy.   So, if it happens again, then you may need to start keeping a log of which foods seem to be causing issues, and stay away from them, at least with the one particular cat.  OR you can try feeding those proteins in a different brand and see if the same thing happens.  If not, then it's probably that Wellness line.