IF they stick to the Japanese schedule Tamamo will have a solo rate up in late April during the CCC pre-event and a second one mid June during onigashima event. She should also be part of the 2020 New Year banner
Again, if they stick to the JP schedule, Jack will have a rate up with Astolfo (who is a 4* which won’t affect jack’s rate up) in mid-November during the Apocrypha event. After that there will be another Apocrypha event with jack on solo rate up in late April 2020...but that is over a year from now.
If you roll for Tamamo in April you should have around three months to save for Nero Caster and then 2.5 months to save for Jack.
Or, save 6 months for Nero, 4 months after that for Tamamo, and 4 months after that for Jack.