If I make animation video from some third party website/app .Then can I use those video for my gig with their watermark ?
A watermark usually indicates you’ve used a free trial of the software to create your video.
Check out their ToS - it’ll probably say that trial (watermarked) videos can’t be used for commercial purposes. You’ll likely need to upgrade to a commercial licence to be able to use it safely.
Other Fiverr users might be inclined to flag your gig if you use a video with a watermark BTW.