If you want the Lightroom adjustments to be included in Photoshop then you need to choose the option to edit a copy that includes the Lightroom adjustments. Otherwise, as you have discovered, you will only get the original image.
Then ... it is not so practical to give vignetting to a TIFF file in Lr ... if I open it in PS and make some modifications.
I think you misunderstood Jims response.
"Edit original" means ignore all your LR edits and open the original file.
"Edit copy with changes" means create a copy of the file that includes all the LR edits and open that file.
In your case you want to use "edit copy" not "edit original".
No ... I understood Jim.
But, I don't want to create a new file.
After editing my TIFFs in Ps, I just want to apply cropping and vignetting to them in Lr (for I could not find a way to make non-destructive post crop vignettings in Ps) ... so I thought that when I make some changes in Ps later, the crops and vignettings in Lr would be stay same.
I don't know why I thought so. I confused this point.
It is clear now, thanks.
In order for Lightroom crops and vignetting etc to remain non-destructive, they would need to be applied to a LR image version AFTER taking the picture into Photoshop, INSTEAD of before.
If it helps, you can reset these properties of the image back to zero (e.g., with a preset). Then Edit in PS (as a copy with adjustments) which having removed the crop, will include the entire original picture area.
Then back in LR, you will see both the original and the edited copy (stacked). You can roll the History of the original image back to the point just before you reset the crop/vignette/whatever, and Copy those settings (just those - selectively). Then you can Paste these (as non-destructive adjustments) back onto the new edited image.
Or, more simply, defer carrying these out in the first place
[My own approach here: that initial adjustments, and then any PS editing, are principally to do with optimising / changing the objective content (using the entire original picture extent). I'd include Upright(?), capture sharpening, white balance and local temperature rebalancing, basic noise reduction, highlight recovery etc since such things work best from original data.
Whatever has to do with presentation (regardless whether an image has been to PS, or not) - it makes sense for that to happen later in the working sequence. E.g., as virtual copies - to explore variations such as different crops or subjective treatments. Any further external changes to the image content can still continue to happen, underlying these variations in a live manner. It's a useful and productive separation IMO.]