First off, I would like to note that I am not a fan of spamming on Twitter, however as a business or as an individual if you want to specifically tweet lots of users about a product or important bit of information then here is how you do it right.
Here is a trick of the trade that won't have users yelling at you for having filled their feed with essentially the same tweet, also this is a great way to actually personalise the tweet to the intended user.
If you want to tweet multiple users to notify them about your important information be sure to mention their Twitter handle first in the tweet and create individual tweets for each. Twitter then see this tweet as a reply/conversation between 2 accounts and therefor it won't show up in other Twitter users feeds unless a user follows each of the accounts.
Example Tweet: Earlier in the year from the #WADay photo campaign
Here @celebratewa have mentioned @tweetperth first in the tweet which means that only users that follow both @celebratewa and @tweetperth would see this tweet in their feed, if a Twitter user followed @celebratewa and not @tweetperth they would not have seen this tweet.
Obviously if a user was to follow the #WADay hashtag or view @celebratewa Twitter profile they would then see all these tweets.
Increase the chances of an action from the user you have tweeted be it retweet, click through, reply, favourite and or follow.
Typically users create tweets that contain all the information about the tweet and then add on as many Twitter handles at the end of the tweet that they can fit in
ie. We have just released our amazing video of our latest product (insert link). Check it out @username @username1 @username2 #hashtag
The Twitter user would then copy and paste the same tweet but then change the usernames mentions. This would then result in all their followers being hit with essentially the same tweet over and over again. So obviously this is a great way to annoy your followers.
So by simply using the Twitter handle of the user you want to tweet first you will be able to send out multiple personalised tweets about your important information without annoying all your followers. Also you will increase the chances of an action from the user you have tweeted be it retweet, click through, reply, favourite and or follow.
In conclusion create a generalised blanket tweet about your important information for all to see and then if you want to create personalised tweets to specific users be sure to mention their Twitter handle first in the tweet. Happy good spamming!