"rightly predicted" is correct and usable in written English.
You can use it when you are referring to a past prediction that came true. For example: "His actions were rightly predicted by the astrologer."
Similarly, the probability for AF presence was rightly predicted in 89% of the cases.
Intended to be affordable and easy-to-wear, Vogue rightly predicted that it would be worn around the world.
As David Cameron rightly predicted, lobbying could become the next great scandal to engulf the political system.
When supertitles were introduced, many opera insiders rightly predicted that the technology would render moot the argument for translating librettos to improve audience comprehension.
The former editor and TV presenter resisted the temptation to gloat after Barton's remarks, but rightly predicted that they would make him a trending topic on the network.
About this time, one of the artist celebrities whom Fry so rightly predicted Cameron would come to outshine, George Frederic Watts, painted a very different portrait of her.
Bob Kerslake rightly predicts a judge-led enquiry into the gross incompetence of every Brexit act: a postmortem will be held.
And although he did rightly predict that 'my time will come', he surely never envisaged this level of popularity.
It is figured out that a surrogate model only rightly predicting the sign of the performance function can meet the demand of HRA in accuracy.
Likewise, one might rightly predict that within A. E. Housman's verses "lad" and "lads" would tabulate more densely than "beauty" or "life" or even "love" or "death".
Can it really be less than three months ago that people were describing Ashworth's position as untenable, with Dame Heather Rabbatts rightly predicting nothing would change if he stayed in charge?
