The newspaper （reported） that despite the increase （in) the minimum wage,

many people (are) still ( having trouble) making ends meet.

供参考

结构是

主句(The newspaper reported) + 名词从句( that many people are still having

trouble making ends meet.

(despite the increase in the minimum wage是短语)

这句子其实与

‘I think that 语主 + 动词+ ...’相同

例子

I believe that you are right.

I believe that, despite some other opinions, you are right.

至於时式方面

可以这样解释

报纸的报告是已经发生的个别事件

所以用过去时

而many people are still ...

则是一般的情况

所以用了现在时