It should ask if you want to install GRUB... that would be terrible if not. Every distro I have used either asks(debian,ubuntu,suse,manjaro) or has a way to disable it(centos I think), or requires you to do it manually (arch).
But if you can't prevent it, you can just fix it later. Bootloaders are easy to change later on Linux systems. Optionally back it up. Then finish the install, and boot up on live or rescue media, and then mount the rootfs and /boot of the one managing grub, and also proc,sys,dev inside the rootfs, and then chroot into the rootfs. Then reinstall grub.
For example set up and enter the chroot with:
mount /dev/sda2 /mnt/root # assuming this is rootfs
mount /dev/sda1 /mnt/root/boot # assuming this is /boot
for d in dev proc sys; do mount -o bind /$d /mnt/root/$d; done
chroot /mnt/root /bin/bash
Then inside the other rootfs, install grub or do other steps:
#optional... especially important if you have modified fstab
# choose one of these depending on distro
mkinitcpio # arch,manjaro
mkinitrd # suse,rh
update-initramfs -u #ubuntu,debian,mint probably
#optional... not required just for grub-install. Required if you have added new kernels or modified /etc/grub.d/ files.
# maybe this will run os-prober for you, saving the step of getting the 2nd OS in the grub menu