This isn't so much a house rule as it is a clarification.  Rules as written are: 

To determine who goes first, second, and so on in a round, each player makes a Speed roll called an initiative roll. Most of the time, it’s only important to know which characters act before the NPCs and which act after the NPCs. On an initiative roll, a character who rolls higher than an NPC’s target number takes their action before the NPC does. As with all target numbers, an NPC’s target number for an initiative roll is three times the NPC’s level. Many times, the GM will have all NPCs take their actions at the same time, using the highest target number from among all the NPCs. Using this method, any characters who rolled higher than the target number act first, then all the NPCs act, and finally any characters who rolled lower than the target number act.

(An initiative roll is a d20 roll. Since your initiative depends on how fast you are, if you spend Effort on the roll, the points come from your Speed Pool.)

The order in which the characters act usually isn’t important. If the players want to go in a precise order, they can act in initiative order (highest to lowest), by going around the table, by going oldest to youngest, and so on.

This is the way that we’ll be interpreting the above rules.

There are basically three initiative chunks.

• Before the NPCs act

• When the NPCs act

• After the NPCs act

Player characters will either act before or after the NPC. There is never a tie.

When the NPCs act is based on the highest level of the NPC.  If there are three level 2 NPCs and one level 5 NPC, the difficulty number for initiative is 5.

A character might be hindered when they roll initiative or they might be able to ease the roll based on a skill, attribute, effort or cypher.  This modified difficulty value determines the target number (difficulty x 3) for that character’s initiative roll.

Roll the target number or higher, and the character gets to go before the NPC, otherwise the character goes after the NPC.

With our example of the team of NPCs with an initiative difficulty of 5, the characters need to roll a 15 or higher to act first.  If one character is trained in initiative, the difficulty for that character (and only that character) is 4 with a target number of 12.  Our trained character could roll a 13 and act before the NPCs while an untrained character rolling a 13 would have to act after.

Roll20

When rolling initiative using a Roll20 Character Sheet, there are two possible options which can be configured by clicking on the show/hide settings gear/cog on your character sheet.  Both feel like they are forcing the Cypher System rules into the Roll20 Turn Tracker.  For the Bumps in the Night game, we will use  the second option: d20+training, effort & bonuses to tracker.

With this option, your training and effort are added to the d20 roll to give you a number that will be added to the turn tracker. For example, if you are trained in Initiative, and roll an 11 on a d20, it will put 14 in the turn tracker. 11 for the roll, and 3 for being trained. Basically each +1 easing of the roll that is done (by skill, effort, assets) will count as a +3 to the die roll when putting it in the turn tracker.