First of all you need to know that there are two different culture values in a city:
1) The culture of the plot the citiy is placed on. This is usually displayed in the game.
2) The culture of the city itsself. It counts the overall generated culture by the city itsself associated to the owner over time.
The culture bonus for espionage mission is based on the second value. The maximum value is -50%

if the spy does have culture in the city and the host does not. It scales linear with the portion of culture between spy and host. Third party culture has no effect.
So how can this happen:
a) The city changes its owner after culture is generated. To generate the bonus the spy can found the city and:
i) Spreads his religion generating culture. If the host has a different state religion it will not generate culture for the host. So one turn with the religion is actually enough for the rest of the game!
ii) Using artists in caste system to generate culture of the spy.
Both do involve gifting the city afterwards. As I said earlier we want to avoid this because it seems to get regulated in pitboss games.
It is helpful to know in war, that this effect often occurs when you capture enemy cities giving the opponent good spots to do missions with the -50% bonus.
but there is another way:
b) The "insert culture" mission. This mission that spreads culture of the spy in the city (2). It spreads 10% of the total generated culture of the city but at least 1

. The requirement for this mission is that there is spy culture on the plot of the city (1)! The cost depends on the amount of generated culture.
To use this, the host founds the spy-city near a city of the spy that will soon get its second (or third) culture expansion. The host never generates any culture in the city. After the culture expansion spreads spy-culture on the plot of the city the spy does a single "insert culture" mission. From now on he gets the full -50% bonus.
There are a few pitfalls to this:
- Creative leaders
- Autospread of the wrong religion
- Any building that generates culture...
I do not konw yet if it might be profitable to spread culture even if the host does generate culture on his own. Maybe this can be explored during the game.