Someone helping me cut out some rotted flooring accidently cut through the top of my engineered (TJI-style) joists (spanning about 14'). Approx 1-2" of the top is cut through. Do I need to now replace these, or add some bracing, etc? Any advice would be greatly appreciated.
Thanks!

Most likely no. To understand this you must understand the install of this system and how it works.
Engineered I joists work on tension and compression. The top of the joist is under compression while the bottom is under tension.
The thin web in the construction simpy provides stability to these two critical members.

During the construction of the home the builder should have glued the top of each one of these I joists to the plywood sub-floor. This helps strengthen the joist. So any cutting into this top chord should do little to effect the way it carries the weight. If however you were to cut into the bottom chord there is nothing to prevent this from pulling apart. Thus causing the floor to weaken.
In your case the damaged I joist is sharing its load of the floor with the ones on each side of it. Providing you have not cut into more then one and the hole caused by the removal of the sub-floor is not so big so you lose the ability of the glued sub-floor from adding support. You should be ok.
As far as adding bracing to this Joist. Not suggested unless the manufactures engineer tells you how to do this. You can not simply fasten any wood to these Joists and make them stronger. There are special methods of nailing and screwing these beams that must be adhered to so not to compromise their strength.

I want to disagree slightly with "The Home Care Club LLC".
The thin web does help provide stability for weak axis buckling of the compression chord, but the major function of the web is to take the shear force. The chords take the tension/compression couple for the bending moment, and the web takes the shear. The real stability of the overall section is provided by plywood being attached to the top chord.

The top is in compression, but cutting through 1"-2" of the top chord (which may just be a 2x) greatly reduces its capacity, because at the section of the cut, it is missing a large % of its section.

While the plywood may, in fact, have been glued to the TJI, I have never come accross another engineer who counts on the plywood for "composite" action.

I would contact the manufacturer and get some typical details from them for this situation. I'm sure it's not the first time they've encountered this.

What is the size of the top chord? How deep are the TJI?

I would agree with you on this but past experiance with this issue on several occasions and reviews with at least one manufacture engineer (not rep who oks everything) has agreed to approve this and provided warranty against failure.

But I must note that the cut was not all the way through on most of them, and the cut was about three to four feet on average from end of joist. Perhaps if the cut was more toward the middle of the joist and the span of the joist was long enough they may not have approve it.

I do agree however fully that the manufacturer should be consulted. Not the factory rep who most of the time gets to handle this type of call.