Yes, you have the theory correct. Consumption "increases" as gov spending does. Then gov spending decreases and the consumption:investment ratio moves towards the investment side.
How does it do this?
I'll save you a lot of time. G + C + I = MAGIC
Keynsian economics was based upon the idea that the free market could lead to "over-production" and "under-consumption" because those who would demand that which was "over-produced" simply don't have enough money to demand it. Thus, the solution is for government to resort to deficit spending to finance projects that mostly pay those now "under-consuming". This "pump-primes" the economy to "get back on track". During this time, taxes and reduced spending are expected to pay for the former deficit spending.
There are a lot of problems with this. For one, government can't simply increase spending without taxing and thus decreasing either consumption or investment. Keynesians assume borrowing money will not reduce consumption and investment, but they don't understand that this can cause price inflation. Also, the later "reduced" government spending doesn't include the debt that needs to be repaid, which means greater taxes and less domestic spending, so basically double less consumption/investment. That's why this phase is always replaced with "military keynesianism". We may never know if true Keynesianism ever works; I don't think we've ever gotten to the debt repayment part of the cycle.
Say's Law refutes that "over-production" can occur. Production is demand for some other form of production. Thus, "over-production" implies "under-production". There is no such thing as aggregate lack of demand.
Pricing according to supply and demand fixes the "over-production"/"under-consumption" "problem". It means deflation of goods that find a surplus. If some producers don't turn a profit under such pricing, then they stop producing such goods and resources are once again attempted to be used in their most desirable arrangement. For some reason, this thought scares the crap out of both politicians and Keynesians, who somehow blame everyone for the malinvestments of some.
Keynesians usually hold "liquidity preference" rather than consumer preference responsible for deflation. Yet, general demand for cash usually only occurs once an economic downturn has already set in. And obviously, deflation can't continue forever, if many people are sitting on money. It must reach an end-point, and a free market will find this point the fastest, then allowing cash demand to fall, and prices to elevate back to "normal" levels (except for the goods that consumers don't want that badly). There are dozens of arguments against this position, many even by (neo)Keynesians.
In short, Keynesianism is a good way to further screw up an already screwed up interventionist market.
For your purposes, just think nominally. Keynesianism doesn't work in real terms. It implies that borrowing (funny) money from foreigners and central banks won't cause price inflation. The whole thing is a money illusion. You don't allow prices to deflate to clear the market; instead you have the government inflate the money supply, so the market is cleared without changing nominal prices (while deflating them in real terms). In that in increases any investment, it creates malinvestment. Only when malinvestment is revealed, Keynesians again sound their siren, demanding inflation - blaming society for not buying the products of "proper" investments at higher cost than they like.