No this is not normal. Something is wrong.
Go into search console. Is your sitemap still running the old sitemap or has it been updated? Is the new domain fully crawled? If your site map is incorrect and 404ing this needs fixing.
Have you done comprehensive 301 redirects to the new domain? How many 404s do you have in search console? Have you used domain forwarding and resolved the urls at the new domain?
Also do you still have the search console with the old domain in it? Look at search analytics (in search traffic), what is your average position? compare to new domain - what is the average position for that. Have you had a big rankings drop? You must have, but this will show you the scale of the problem.