I don't know about talking in context, but my cockatiel certainly understands in context(he doesn't talk). Let me copy and paste from what I wrote in another thread:
"Oh, young tiels and early stages of bonding, I remember those days. <3
Alex doesn't have many tricks, just practical things we have learned together thru the years(never really "trained" him trained him. I was only 11 when I got him.).
He knows "hold"(turbulence expected, hang on tight buddy), step(ususally I snap twice before presenting my finger and telling him to step), shoulder, put your wings down, show me your foot, other foot, gimmie five, show me your wings, what are you doing, where are you, ay quit that!, I'll be right back, I'm only going over here, etc etc etc. I more talk to him than give commands, and he seems to understand quite a bit from context. For example the other day he found a comfy perch on a weird wall we have in the bedroom between the bedroom proper and a weird 2 person bathtub(no door between, and the "wall" has holes in it like a window but with no pane, the mobile home came with the property so the weird "[jacuzzi] tub" freaks us out a bit... we converted it into an enclosure for our tortoise. Lmao). I told him fine, you can stay there but no eating the wall! After a bit he started chewing the wall and I was like, "hey! What was our deal?" And he gave me this look like, oop! I'll be good, mom. And quit eating the wall. Now he only "eats the wall" when he wants something and I am ignoring him(food, whatever I'm eating, water, bedtime). If he wants food that I'm eating super badly, he will waddle his happy butt on over and try to steal it(Alex has never been much of a flyer).
The other day I watched him pick up the paper towel bedding, hold it with his foot and peck at something under the bedding. I wanted to test if he knew what he was doing so I moved him, and put a small amount of millet under the paper towel. He pretended to be busy elsewhere, and then slowly went back to the spot, watching me all the while, pretending to be distracted along the way when he caught me looking, and then finally waddled straight to the spot with the millet and repeated the pick up towel, hold with foot, eat the food action. WOW. Object permenance, object manipulation, comprehention of the mind on an "other" and that the "other" may have different thoughts about him taking the food... just wow. Even having known this bird for 17 years, he surprises me with his mind all the time, and remember: Tiels are supposed to be on the "stupider" side of parrot intelligence. It just blows me away. Parrot cognition is FASCINATING to me. "
Freedom also seems to understand a lot(blue and gold macaw). When she came to us she knew "mmmmm"(anything edible), and she asks for tasty things like that. She knows "wanna scratch?" And asks for scratches like that. She understands what "wanna" means, and I have used it like, "wanna mmmm?" "Wanna come out?" And she seems to understand. She *right away* picked up when I said "wanna mmm? Go home, get down on your perch" and has also understood "wanna come out? Get on your perch". Obviously understands cause and effect like that. I did not target train her or anything like that, and as far as I know her previous owners did not either.