I scheduled the import job using curl, but it doesn't update the entries. If I visit the link in browser, it works fine.
Seems like your crontask isn't configured correctly.
1) Verify your curl statement works properly by running it in Terminal (Mac) or Putty (Windows).
2) Verify you're configuring your crontask correctly. Are you storing it in the right file (or configuring it correctly in Plesk?). Consult your hosting company if need-be.