Parola will print the c-string you pass it. If you give it another string, you will clear the previous one and display the new one. This is something you have already discovered.
So you need to build up your message in the c-string and the display the complete message instead of doing a sequence of .print statements. I would suggest that you learn about the sprintf() function. Something like
char charBuffer[sizeOfBuffer];
sprintf(charBuffer, "%02d:%02d:%02d", hourVariable, minuteVariable, secondVariable);
is what you need to get to. This will print the time in hh:mm:ss with leading zeros on the digits. If you read the documentation for sprintf it will make sense.
You can then .print charBuffer or use one of the animations.