From Pottermore:

The Mirror of Erised is one of those magical artifacts that seems to have been created in a spirit of fun (whether innocent or malevolent is a matter of opinion), because while it is much more revealing than a normal mirror, it is interesting rather than useful. Only after Professor Dumbledore makes key modifications to the mirror (which has been languishing in the Room of Requirement for a century or so before he brings it out and puts it to work) does it become a superb hiding place, and the final test for the impure of heart.

The mirror’s inscription (‘erised stra ehru oyt ube cafru oyt on wohsi’) must be read backwards to show its true purpose.

#J.K. Rowling’s thoughts Albus Dumbledore’s words of caution to Harry when discussing the Mirror of Erised express my own views. The advice to ‘hold on to your dreams’ is all well and good, but there comes a point when holding on to your dreams becomes unhelpful and even unhealthy. Dumbledore knows that life can pass you by while you are clinging on to a wish that can never be – or ought never to be – fulfilled. Harry’s deepest yearning is for something impossible: the return of his parents. Desperately sad though it is that he has been deprived of his family, Dumbledore knows that to sit gazing on a vision of what he can never have, will only damage Harry. The mirror is bewitching and tantalizing, but it does not necessarily bring happiness.

From what I can make of these passages, it seems that Albus made some modifications, before "bringing it out" of the room of requirement nearly a century ago. Harry Potter takes mostly takes place in the 1990's. An exact century before would be in the 1890's, but since it doesn't have to be exact and/or because perhaps the timeline of the Fantastic Beast films will be slightly altered, we can suppose that he may have modified the mirror either earlier than shown in the film or he may have yet to...

#"It shows nothing more or less than the deepest desire of our hearts. - Albus Dumbledore"

With that being said, nowhere is it stated that the mirror will not show you the past, as there could easily be something from the past that someone may desperately desire, which is what the mirror shows it's viewer.

From Pottermore:

The Mirror of Erised is one of those magical artifacts that seems to have been created in a spirit of fun (whether innocent or malevolent is a matter of opinion), because while it is much more revealing than a normal mirror, it is interesting rather than useful. Only after Professor Dumbledore makes key modifications to the mirror (which has been languishing in the Room of Requirement for a century or so before he brings it out and puts it to work) does it become a superb hiding place, and the final test for the impure of heart.

The mirror’s inscription (‘erised stra ehru oyt ube cafru oyt on wohsi’) must be read backwards to show its true purpose.

#J.K. Rowling’s thoughts Albus Dumbledore’s words of caution to Harry when discussing the Mirror of Erised express my own views. The advice to ‘hold on to your dreams’ is all well and good, but there comes a point when holding on to your dreams becomes unhelpful and even unhealthy. Dumbledore knows that life can pass you by while you are clinging on to a wish that can never be – or ought never to be – fulfilled. Harry’s deepest yearning is for something impossible: the return of his parents. Desperately sad though it is that he has been deprived of his family, Dumbledore knows that to sit gazing on a vision of what he can never have, will only damage Harry. The mirror is bewitching and tantalizing, but it does not necessarily bring happiness.

From what I can make of these passages, it seems that Albus made some modifications, before "bringing it out" of the room of requirement nearly a century ago. Harry Potter takes mostly takes place in the 1990's. An exact century before would be in the 1890's, but since it doesn't have to be exact and/or because perhaps the timeline of the Fantastic Beast films will be slightly altered, we can suppose that he may have modified the mirror either earlier than shown in the film or he may have yet to...

#"It shows nothing more or less than the deepest desire of our hearts." - Albus Dumbledore

With that being said, nowhere is it stated that the mirror will not show you the past, as there could easily be something from the past that someone may desperately desire, which is what the mirror shows it's viewer.