the shul i davened in actually didn’t say tachnun on monday either
shmuel hanavi’s yahrtzeit
addtionally the reason we don’t say tachnun on beis sivan is because it’s in between rosh chodesh and shlosha yimei hagbalah
therefore one shouldn’t say tachnun on erev rosh chodesh, it’s in between yom yerushalayim and rosh chodesh