My family will be trying to go to these restaurants while already in the parks or straight from the to return. How strict r the dress codes?
At Tiffins, I was there in shorts and a t-shirt and didn't have any problem, so was pretty much everyone else in the restaurant. You should be good.
Anything in the parks has the same dress code as the parks in general... they don't expect anyone to leave the park to change clothes for dinner. It's just a few of the signature restaurants at resorts that have a real dress code.
For Narcoossee's the men will need to wear a collared shirt with dress shorts or pants. Women can wear a dress, a blouse or nice sleeveless shirt (like would be appropriate in an office... not a tank top or spaghetti straps) with dress pants/shorts or a skirt. No t-shirts, jeans, cargoes, or flip flops for anyone, and only closed shoes for men.
I've only ever worn a dress, and only gone with women but I've never seen anyone who was dressed more casually, so either nobody tried or they were turned away. If you don't have time to change before then I'd suggest a nice summery dress (I wear maxi dresses at WDW all the time) for the ladies and dress shorts and a lightweight short sleeved button-down for the gents. You can be dressed well and still be comfortable in the parks.
We like to make dinner at these restaurants an occasion so I asked about dress code after an incident at CG (long story which is not relevant here) I was told by Disney that Narcossees had a strict dress code i.e. they applied the dress code more than CG although the published dress code is the same I think. Therefore if we needed an 'occasion' we should consider eating there