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The red-haired girl is a witch.
Everybody calls Anne "that red-headed witch" at least once after she comes to Green Gables. Nobody means it in the old sense, because in the strictly Presbyterian world of Prince Edward Island, witches in the old sense don't exist.
It's true anyway.
When Matthew Cuthbert dies, Anne's grief is so strong that it rolls time back to the happiest day of her life: the day she learned she could stay at Green Gables. She can't bring Matthew back, because even Anne's imagination isn't that strong... but without realizing it, in her blind grief she can hold the whole of Avonlea still at a single point in time relative to the outside world, while its own life ticks on unimpeded.
When Anne learns years later that Marilla is going blind, and decides to stay at Green Gables to teach school rather than attending Queen's, she takes charge of her life again. She marches forward, and time shakes itself and marches in her train.
When Marilla and Mrs Rachel Lynde cook up their plan to move in together and free Anne to go to Queen's, Anne is so excited that she flips her personal timeline back to the previous year's "fork in the road", taking the other branch now - schoolteaching first, then her Freshman year at Queen's, both take place at the same time. The same thing happens again when her wedding matches up with the time right after she finishes Queen's: Gilbert doesn't realize it, but because his life is so closely entwined with Anne's, his three years at medical school both take forever and pass in no time at all.
After her wedding, Anne is utterly blissful and looking forward to new experiences again, so time obliges by sweeping along normally - though still out of all sync with the outer world's timeline - as she travels to Four Winds and starts building a home there with Gilbert. She makes new friends and plans for the future; only occasionally during that first summer does she stop the communal clock of Four Winds, while Avonlea (its temporal matrix sighing with relief at Anne's departure) speeds forward to rejoin the rest of the world.
Little Joy's death is so unprecedented that Anne freezes time, until she heals from her first grief, but can't roll time back because there is no comparable event for her mind to latch onto. She could have rolled Jem's birth back a year to match up the birth of her first child with that of her first surviving child, but she doesn't; she keeps Joy in her memory as an individual, and Jem starts to grow up in his own proper time, or as close to it as any of Anne's children can get.
Anne is maturing fast, learning to live in linear time without marking each "fork in the road" so as to return to the ones that she misses... but there's one more major change to come before she can let her world march smoothly on to rejoin the timestream. The loss of Captain Jim, her second most beloved father figure, takes her badly, and even though she tries her best to grieve him well and be glad that he finished reading his book before he left -- that first moment of dread, as she runs along the beach to the lighthouse under the relentless sweep of the still-burning light, flings her back literally as well as metaphorically to the day that Matthew died.
Anne's children grow up, after that, more or less in the slow linear march of displaced time from the 1890s onward. It's only the Great War - the war to end all wars, the war that seemed over and over as if it would never end - that can force itself at last into everyone's timestream, aligning the years, and cannot be rewound or avoided or replaced. It takes Anne's son instead of her husband, but that is the only concession it makes.
After Walter's death, Anne never changes time again. She's learned her strength and its limits by now, and she teaches Una (too young, the War made everyone grow up too young) that rewinding the War can't bring anyone back. It will only send more and more young men to their deaths. The Great War won't end, can't end, doesn't end until every time-witch in the world has learned that lesson, but Anne - the strongest of them all - could have extended it forever if she'd chosen to mourn her boy that way.
She's finally strong and wise enough not to do so.