My cat keeps pooping NOT in the litterbox?

I have a 10 year old male Siamese, neutered. He's a sweetheart, but a little shy at times, and not very playful. Recently, our house is being worked on from the inside, so the the cats are in our extra room with food, water, and a litter box so they don't get hurt. Just to clarify, this is where their necessities were always kept, and this is nothing new for them. They've been kept in the room before, too. Now, I went in the room to chill with the cats for a little, and right when I was going to the door, he began to meow. I assumed it was because he wanted out, but then he "did his business" right in front of me. He's pooped out of the litter box before, like when he meets new people (I assume he gets stressed very easily) but nothing was happening to scare him. He repeated this action several times again when I came in to spend time and fill their bowls. Just today, I was playing with the other cat in the room, and the toy I was using made some noise. My siamese was laying in bed when his eyes got all bloodshot, and he pooped in his own bed, and lay back down. I shooed him away from the feces, but it was strange nonetheless. Can anybody help me here? I've been reading that pooping out of fear for cats is caused by abuse or extreme actions, but nothing that's happened could even be considered "abuse" or "extreme". Does anybody have any idea what may be going on?

It sounds like he may not be well. I would really recommend a vet check before looking at behavioral issues.

Yes, he's very stressed.  I would recommend two things.  First, invest in a Feliway diffuser or some other calming agent like Rescue Remedy.  This will help him de-stress.  Also, add an additional litter box.  Be sure to clean the spots on the floor with an enzymatic cleaner.  Be sure that there are familiar smelling things in the room like some of your worn clothes with your scent on them and bedding. If possible, close off the areas where the work is being done and let them out of their room until the work resumes.