When is a timestamp (auto) updated?

I think you have to define the timestamp column like this

CREATE TABLE t1 
(
    ts TIMESTAMP DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP
);

See here

An auto-updated column is automatically updated to the current timestamp when the value of any other column in the row is changed from its current value. An auto-updated column remains unchanged if all other columns are set to their current values.

To explain it let's imagine you have only one row:

-------------------------------
| price | updated_at          |
-------------------------------
|  2    | 2018-02-26 16:16:17 |
-------------------------------

Now, if you run the following update column:

 update my_table
 set price = 2

it will not change the value of updated_at, since price value wasn't actually changed (it was already 2).

But if you have another row with price value other than 2, then the updated_at value of that row (with price <> 3) will be updated to CURRENT_TIMESTAMP.

Give the command SHOW CREATE TABLE whatever

Then look at the table definition.

It probably has a line like this

logtime TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,

in it. DEFAULT CURRENT_TIMESTAMP means that any INSERT without an explicit time stamp setting uses the current time. Likewise, ON UPDATE CURRENT_TIMESTAMP means that any update without an explicit timestamp results in an update to the current timestamp value.

You can control this default behavior when creating your table.

Or, if the timestamp column wasn't created correctly in the first place, you can change it.

ALTER TABLE whatevertable
     CHANGE whatevercolumn 
            whatevercolumn TIMESTAMP NOT NULL
                           DEFAULT CURRENT_TIMESTAMP 
                           ON UPDATE CURRENT_TIMESTAMP;

This will cause both INSERT and UPDATE operations on the table automatically to update your timestamp column. If you want to update whatevertable without changing the timestamp, that is,

To prevent the column from updating when other columns change

then you need to issue this kind of update.

UPDATE whatevertable
   SET something = 'newvalue',
       whatevercolumn = whatevercolumn
 WHERE someindex = 'indexvalue'

This works with TIMESTAMP and DATETIME columns. (Prior to MySQL version 5.6.5 it only worked with TIMESTAMPs) When you use TIMESTAMPs, time zones are accounted for: on a correctly configured server machine, those values are always stored in UTC and translated to local time upon retrieval.