Ok, I think you have to read TTWCTT in partnership with When Hitler Stole Pink Rabbit.
It is a young girl's attempt to understand the loss of her former life.
The tiger, Nazi's, invade the home, initally seeming threatening but being absorbed into the family and normalcy, this refers to those who failed to fully recognise the threat and remained in Germany and were killed, the family friend in WHSPR.
The tiger gradually removes everything good from the family, food, access to water (allegory for freedom of movement etc).
Father returns home, recognises true risk and has a good plan, to flee, that's why Sophie is in her nightie. Cafe represents Paris, where Judith Kerr and her family initally fled to; but as said previously fomesti cat and dark man in the background on the journey there represent the ongoing threat.
Purchase of tiger food indicates, we must never forget.
I think it is significant that the Tiger looks so much like the Nazi 'cats' in Maus and think there is some shared artistic view there...