If it is an automatic process does the process happen without the user pressing the button or do they have to trigger it?
Either way I would try to phrase it more around refreshing the table to represent the most accurate up to date information rather then say anything about re-arranging or re-sequencing. Unless it is significantly important for the users to know that items are being re-ordered a certain way I would try to frame it as: “Some data may be out of date, please refresh to view the most accurate information.” (where “refresh” is a button or text link)
Of course if it is an automated process that doesn’t require user intervention you could just just do it so that it is always up to date whenever they load the table (or I suppose give them the refresh menu if they keep the page open for a significant amount of time).
For the message text itself: “Re-sequencing items required, press update button” is completely different to “items need to be re-arranged”. It implies that pressing the update button will be enought to get the re-sequenced items. But your explanation means that the user need to move items around.
If you mean that the items will be re-arranged automatically once the user pressed update, then a message like “Press ‘update’ to automatically re-sequencing the items” is a better solution. Still, this is probably not the best approach. Perhaps the user also needs to know WHY the items need to be re-arranged?
The ‘reload’ button seems the most relevant. Two circling arrows is a common representation. Animate or highlight the icon when a refresh is needed… no words are necessary.