这个句子时态确实有误，要么改为一般过去时或现在完成时，要么改为现在进行时或一般将来时。manage to do并非只能用于过去时，也可以用于将来时的。例如以下COCA语料库例句：

I am curious how they will manage to keep it together as this escalates by the week.

The real question is how the traditional companies like Sony and Microsoft will manage to compete and stay relevant as new disruptive players enter the market.

I got a really good feeling that I will manage to fix my shoulder 100% with no surgery involved.

用现在进行时也是可以的：

I know Jenny is managing to find humor in them, but they do rather disturb me.

One Republican aide says the president is managing to screw up his campaign by an attack on the speaker, Paul Ryan.

What we don't know is how the rest of the world is managing to do a better job of teaching its children.