DNS-Settings on Network-Manager when using VPN

I googled here and have exactly the same issue too. (Ubuntu 19.04)

For me, this answer solved.

nmcli c modify <vpn-settings-name> ipv4.dns-search '<domain>' 

You should specify <vpn-settings-name> that corresponds to a VPN setting name in GUI. And <domain> is the domain name you want to search via DNS in the remote network.

After reconnecting to VPN, systemd-resolved status ppp0 shows

Link 6 (ppp0)
      Current Scopes: DNS
DefaultRoute setting: yes
       LLMNR setting: yes
MulticastDNS setting: no
  DNSOverTLS setting: no
      DNSSEC setting: no
    DNSSEC supported: no
  Current DNS Server: 192.168.1.1
         DNS Servers: 192.168.1.1 (<--- my dns)
                      192.168.1.10
          DNS Domain: corp