What it comes down to is different meanings of the world reality.
In this exchange between <PERSON> and Dr. <PERSON>
<PERSON>: What is your job exactly? Besides making balloon animals.
Dr. <PERSON>: Protecting your reality, douchebag.
But Dr. <PERSON> isn't referring to reality as the sum total of all of existence. He is only referring to the dimension they live in.
In Doctor Strange we see <PERSON> opening the Eye of Agamotta and manipulate time. When confronted by <PERSON> and <PERSON> about the dangers of doing this <PERSON> asks what the real purpose is in studying the mystic arts. <PERSON> explains that:
While heroes like the Avengers protect the world from physical dangers we sorcerers safeguard it against more mystical threats. The Ancient One is the latest in a long line of Sorcerers Supreme going back thousands of years to the father of the mystic arts the mighty <PERSON>.
<PERSON> further states
<PERSON> built three Sanctums in places of power where great cities now stand. Together the Sanctums generate a protective shield around our world. 194
The Sanctums protect the world and we sorcerers protect the Sanctums.
<PERSON>: From what?
<PERSON>: Other dimensional beings that threaten our universe.
In other words, the Time Stone as the Eye of Agamotto helps the Sorcerer Supreme protect this dimension or reality from other dimensional threats. As seen in Doctor Strange it is used to make <PERSON> stop his attack on our dimension so it does work as advertised.
As to how the Time stone can be used against the Reality stone there is the following. In Avengers: Infinity War we see Dr. <PERSON> use the Time stone to see the future. Afterwords the following exchange takes place:
<PERSON>: I went forward in time to view alternate futures. To see all the possible outcomes of the coming conflict.
<PERSON>: How many did you see?
<PERSON>: 14,000,605.
<PERSON>: How many did we win?
<PERSON>: One.
So the Time stone has allowed Dr. Strange to see a possible victory. The scene ends there and when the movie comes back to that group of characters it is when <PERSON> arrives to take the Time stone. If Dr. <PERSON> has explained how they could win it was done off screen and we won't know how it could happen until Avengers: Endgame. 786